Question

Solve |4-7x| -5 less than 8

Please select the best answer from the choices provided

A
B
C
D

Answer 1

Choice B is the correct answer.

Explanation:

We have given an inequality.

|4-7x| -5 < 8

We have to find the solution of given inequality.

Adding 5 to both sides of given inequality, we have

|4-7x| < 8+5

|4-7x| < 13

Applying absolute value rule, we have

-13 < 4-7x < 13

-13-4 < -7x < 13-4

-17 < -7x < 9

By dividing to -7 , reverse the inequality

-9/7 < x < 17/7

Hence, the solutions are x < 17/7 or x > -9/7.

Answer 2

b. {x l -9/7 < x <17/7}

Explanation:

l 4 - 7xl -5 < 8

Adding 5 on both sides, we get

l4 - 7xl < 13

Absolute function has two values.

{ 4 - 7x < 13 and (4-7x) > -13}

Now let's solve for x.

-7x < 9 and -7x > -17

x > -9/7 and x < 17/7

Now we have to combine the two inequalities and write the solution

{x l -9/7 < x <17/7}

Answer: b. {x l -9/7 < x <17/7}

Hope this will helpful.

Thank you.