Find the value of a for which the solution of the inequality is all real numbers

a(x + 3) < 5x + 15 - X

Answers

Answer 1

Answer:

x = 3

Step-by-step explanation:

 (3 • (5x - 15)) -  15 • (x - 3)  = 0  

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  5x - 15  =   5 • (x - 3)  

Equation at the end of step

3

:

 15 • (x - 3) -  15 • (x - 3)  = 0  

STEP

4

:

Pulling out like terms

4.1      Pull out     15  

Pulling out like terms :

4.2      Pull out     x-3  

After pulling out, we are left with :

     15 • x-3 • ( 1  *  1 +( (-1)  *  (-1) ))

Equation at the end of step

4

:

 30 • (x - 3)  = 0  

STEP

5

:

Equations which are never true

5.1      Solve :    30   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

5.2      Solve  :    x-3 = 0  

Add  3  to both sides of the equation :  

                     x = 3

One solution was found :

x = 3

Answer 2

The required value of a for which the solution of the inequality is all real numbers is a > 4.

What is inequality?

A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now the given inequality is,

a(x + 3) < 5x + 15 - x

or, a(x + 3) < 4x + 15

Now let us solve for x first,

⇒ ax + 3a  < 4x + 15

Subtract 3a from both sides we get,

ax < 4x + 15 - 3a

Subtract 4x from both sides we get,

ax - 4x < 15 - 3a

or, (a - 4)x < 15 - 3a

Dividing both the side by (a - 4) we get,

x < (15 - 3a) / (a - 4)

Now for solutions to be real numbers,

a - 4 > 0

subtracting 4 both the side we get,

⇒ a > 4

this is the required value of a for which the solution of the inequality is all real numbers

Thus, the required value of a for which the solution of the inequality is all real numbers is a > 4.

To learn more about inequality :

https://brainly.com/question/13363104

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Related Questions

How many solutions does the following equation have? -6(x + 7) = -42 - 2​

Answers

Answer:

x = 1/3 or .333

Step-by-step explanation:

What is the area of the triangle?

Answers

Answer:

4

Step-by-step explanation:

The formula of the area of a triangle is 1/2 times base times height

1/2 .4.2 equals 4

James has $40 to spend. He wants to buy 2 tickets to a show. He has to spend $7 to get where tickets are sold. The following inequality can be used to find out the highest price James can afford to pay for each ticket. 2x+7 less than or equal to 40.
A.) x less than or equal to 23.5
B.) x less than or equal to 16.5
C.) x greater than or equal to 23.5
D.) x greater than or equal to 16.5

Answers

Answer:

B.) X less than or equal to 16.5

Step-by-step explanation:

If you take his limit, 40 and subtract the 7 dollars you will get 33. Then, divide that by two because he will need two tickets and you will get 16.5. It can't be greater than 16.5 because he will go over his budget.

Answer:

x ≤ 16.5

Step-by-step explanation:

40 ≤ 2t + 7 Subtract 7 from both sides.

40 - 7 ≤ 2t + 7 - 7

33 ≤ 2t Divide both sides by 2.

[tex]\frac{33}{2}[/tex] ≤ [tex]\frac{2t}{2}[/tex]

16.5 ≤ t or t ≥ 16.5

answerrrr plssssssssssssssssssssssssssssssssssss

Answers

Answer:

c

Step-by-step explanation:

because like it would happen in real life yk and the others dong make sense at all

tell me if its right

Answer:

c)scene

according to me

What is the equation of the vertical line through -8, 5

Answers

Answer:

The answer of the following questions is y=3x-19

What is 4÷97 answered as a decimal?

Answers

Answer:

0.0412371134

Step-by-step explanation:

Answer:

24.25 hope that helps

Step-by-step explanation:

y=-3x-1 find slope and y interceapt

Answers

Answer:

Slope = - 3

y-int = - 1

Step-by-step explanation:

Understanding slope intercept

y = mx + b

y = Slope(x) + y-intercept

y = -3x - 1

y = (-3)x + (-1)

Slope = - 3

y-int = - 1

Hope this helps,

find the difference
5/6-7/10​

Answers

Answer:

2/15

Step-by-step explanation:

BRANIEST PLS

Answer: 2/15 is the answer hope this help

Step-by-step explanation:

I WILL GIVE BRAINLIEST AND 36 Points
Refer to screenshots

8. Which line on the graph represents the equation y=3x-2?
line A
line B
line C
line D

9.Which equation represents the graph?

y = |x| – 4

y = |x – 4|

y = |x + 4|

y = |x| + 4

12.Which equation represents the graph?

y = |x| + 6

y = |x – 6|

y = |x| – 6

y = |x + 6|

17.Which set of ordered pairs corresponds to the graph?

{(5, 1), (4, 2), (0, –1), (–2, 3), (–5, 1)}

{(–2, 3), (5, 1), (–5, 1), (1, 0), (4, –2)}

{(–5, –1), (–2, 3), (0, –1), (4, –2), (5, 1)}

{(–2, 4), (–1, –5), (–1, 0), (1, 5), (3, –2)}

19.Which equation is represented by the table?
Y=-|X-1|-4
Y=|X-1|-4
Y=-|X+1|-4
Y=|X+1|-4

Answers

Answer:

1.a

2.c

3b

4.c

5.a or b

Step-by-step explanation:

Patulong naman sa business math HAHHA

Answers

English mam ahahahhahahahahahha
Yeydhdurufjfjfjfifjfufufufufufururesa fududucigiv fjdhdudueuc cjcjcjdhducuc cjcjcjd

Car Y travels 105 miles on 3 gallons of petrol. Car Z travels 80 miles on 9 litres of petrol.

Which car has better petrol consumption ( more miles per gallon)?

You may use the fact that 1 gallon =4.5 litres


Options are

A. None

B. Y

C. Z

Answers

Answer:

Car Z has better petrol consumption. Choice C. Z

Step-by-step explanation:

Petrol Consumption

Car Y travels 105 miles on 3 gallons of petrol. The average consumption is 105 / 3 = 35 miles/gallon

Car Z travels 80 miles on 9 litres of petrol. Since 1 gallon=4.5 litres, the consumption of car Z is 9/4.5= 2 gallons. The average consumption is 80/2 = 40 miles/gallon.

This means that car Z has better petrol consumption. Choice C. Z

how do you do this ??​

Answers

Answer:

Step-by-step explanation:

There are my notes for that stuff. I hope you understand cause I'm having trouble with it too. Just ask any questions if you still need help maybe i can help.

Are any of these numbers an Integer?
15
20/5
44
13/19
-35.47
;w; help

Answers

Answer: 15, and 44 are integers.

Step-by-step explanation: For 15 to be an integer, 15 has to be a whole number. Furthermore, for 15 to be an integer, you should be able to write 15 without a fractional or decimal component. 15 is a whole number that can be written without a fractional component, thus 15 is an integer, as well as 44.

15 and 44

An integer is a whole number that is not a fraction since all the other numbers are not a whole your answer is 15 and 44.

Both questions in picture! Will give brainliest!!

Answers

Answer:

See belolw

Step-by-step explanation:

[tex]P=53\text{ft}[/tex]

[tex]P = a+b+c[/tex]

[tex]53=2x-15+x+1+3x-29[/tex]

[tex]53=6x-43[/tex]

[tex]96=6x[/tex]

[tex]x=16[/tex]

[tex]a=2x-15[/tex]

[tex]a=2(16)-15[/tex]

[tex]\boxed{a=17}[/tex]

[tex]b=x+1[/tex]

[tex]b=16+1[/tex]

[tex]\boxed{b=17}[/tex]

[tex]c=3x-29[/tex]

[tex]c=3(16)-29[/tex]

[tex]\boxed{c=19}[/tex]

Answer:

1. x=16, a=17, b=17, c=19

2. k=-2

Step-by-step explanation:

1.

We can set up an equation where all the labeled sides add up to 53, and then find x:

(2x-15)+(x+1)+(3x-29)=53

6x-43=53

6x=96

x=16

Now that we know x, we can plug it back in to the expressions of the triangles to find their side lengths:

a=2(16)-15=17

b=16+1=17

c=3(16)-29=19

2.

Reminder: the slope of a line is its change in y over its change in x. We can then set up an equation:

[tex]\frac{2-k}{k-(-3)}=4\\\frac{2-k}{k+3}=4\\2-k=4k+12\\5k=-10\\k=-2[/tex]

please answer this I really need help if you just take my points ill report I just need help pleassesssseessesesee!!!!!!!! (15 points!)

Answers

Answer:

1.b 2.a      i hope this is right

Step-by-step explanation:

14:6 divided by 5 ( the 14:6 is a ration )

Answers

Answer: 7/15
Explanation: always remember that a ratio is the same as a fraction. Convert 14:6 into a fraction then divide it by 5. Don’t forget to take the reciprocal.. just take a look at the pic

A shop sells bagels for $5 per dozen. You can use the table to answer
the questions. Explain your reasoning. (Show all your work)

1. At this rate, how much would 6 bagels cost?

2. How many bagels can you buy for $50?

Answers

Answer with step-by-step explanation:

Lets says the number of bagels is B and the price in dollars is D.

Equation: D × 12/5 = B

1. 6 is half of a dozen, which means the price would be half of 5, 2.5

2. $50 is 10× the amount of $5, so the amount of bagels would be 10 × 12, which is 120 bagels.

Hope this helped! (brainliest please)

A Dozen mathematically means 12.

It is important to note that:

$5 = 12 bagels

1) 12 bagels = $5

          6 bagels = ?

Cross Multiply

6 bagels  x $5 / 12

= $7.50

Therefore, 6 bagels would cost $7.50

2) $5 = 12 bagels

         $50 = ?

Cross multiply

$50 x 12 bagels / $5

= 120 bagels

Therfore, you can buy 120 bagels for $50

To learn more, visit the link below:

https://brainly.com/question/9094069

Which of the following statements does not represent the same value as the others?

the distance between 0 and −9
the absolute value of negative 9
the opposite of 9
the absolute value of 9

Answers

the distance between 0 and −9

the absolute value of negative 9

the opposite of 9

the absolute value of 9

Please help me please I feel like crying cause I can't do it...

Answers

Answer:

1. 39

2. 15

3.329

4. 16

5. 300

Step-by-step explanation:

Just divide the first two numbers and then multiply the quotient by the last number. You'll be ok, you've got this, keep your head up!

1. 52/4 = 13 and 13 x 3 = 39

2. 45/9 = 5 and 5 x 3 = 15

3. 470/10 = 47 and 47 x 7 = 329

4. 10/2.5 = 4 and 4 x 4 = 16

5. 125/2.5 = 50 and 50 x 6 = 300

The water level at Lake Livingston last week was 3.45 inches below sea level. After a heavy rain, the lake measured 2.9 inches above sea level. What was the change in the water level?

Answers

Answer: -0.55

Explanation:2.9 - -3.45 = -0.55

Pls give brainless

Easy 7th grade work sheet ! Please help , I’ll give brainliest (all answers)

Answers

1. +16
2. -11
3. -6
4. 9
5. 8
6. 5
7. Simply place dots on the numbers stated, which are 11, -5, and -8.
8. The absolute value of a non-zero number is positive because absolute value is a magnitude, and is either positive or zero. The absolute value of any non-zero number can be thought of as its distance from zero, which will always be positive.

Please mark as branliest if i helped!!:)

If Mariana scores 5 points how many points did aki score

Answers

There is no graph or further explanation for a question to answer

Jason had one hundred fifty-nine dollars to spend six books.After buying them he had fifteen dollars.How much did each book cost.

Answers

Answer:

11.5

Step-by-step explanation:

Divide: 159:6-15

Calculate: 26.5-15

\\11.5//

Answer:

24.8333 with 3 repeating.

Step-by-step explanation:

Lets make an equation for this.

159 - x = 15

X is what we are loooking for so lets isolate it.

Subtract 159 on both sides.

-x = -149

Since both are negative we need to simply cross it out.

x = 149

Now he bought six books, so divide 149 by 6.

You would get 24.8333 with the 3 repeating.

What is the equation of the line that passes through the point (1,0) and has a slope
of 1?

Answers

Answer:

x=y

Step-by-step explanation:

The answer is x=y if the slope is 1,1 | 2,2 | 3,3 | etc

Hello pls helppppppppppp

Answers

Answer:

B

Step-by-step explanation:

Answer:

For example, if we multiply the numerator and denominator of 2/3 by 4 we get. 2/3 = 2×4 / 3×4 = 8/12 which is an equivalent fraction of 2/3. t is 12/20 Simplified? - 3/5 is the simplified fraction for 12/20.

How do i simplify the expression 6(x+2)-4

Answers

Answer:

It would be 8

ASAP WILL GOVE BRAINLIEST FO YOU EXPLAIN AND GIVE ME ANSWER ASAP

Answers

Answer:

[tex]105 \frac{3}{10}[/tex], so most likely G

Step-by-step explanation:

[tex]105.3=105.30=105 \frac{30}{100} =105\frac{3}{10}[/tex]

First, we convert to a fraction. Then, we simplify.

Someone plz answer

the school jimmy goes to is selling tickets to a fall musical. om the first day of ticket sales the school sold 9 adult tickets and 14 child tickets for $101. The school took in $88 on the second day by selling 12 adult tickets and 7 critical tickets. What is the price each of one adult ticket and one child ticket.

Answers

Answer:

if my math is correct it is $4.39

Step-by-step explanation: do not fully trust this

-0.6 repeating terminating or neither

Answers

Answer:

Repeating.    

Step-by-step explanation:

i think it is repeating.


can Yhu help me plzzz!!!!

Answers

Answer:

f^-1 (x) =7 − 21x

Step-by-step explanation:

Hope this helps!

Plz give brainliest

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