Question

Solve for x.

|4x - 5| < 7

x < 3 and x > -1/2 correct?
x > 3 or x < -1/2
x > -3 or x < 1/2
x < -3 and x > 1/2

Answer 1

Remove the absolute value term. This creates a ± on the right-hand side of the equation because |x|=±x.

4x−5<±(7)

Set up the + portion of the ± solution.

4x−5<7

Move all terms not containing x to the right-hand side of the inequality.

4x<12

Divide each term in the inequality by 4.

x<3

Set up the − portion of the ± solution. When solving the − portion of an inequality, flip the direction of the inequality sign.

4x−5>−(7)

Multiply −1 by the 7 inside the parentheses.

4x−5>−7

Since −5 does not contain the variable to solve for, move it to the right-hand side of the inequality by adding 5 to both sides.

4x>5−7

Subtract 7 from 5 to get −2.

4x>−2

Divide each term in the inequality by 4.

x>−12

The solution to the inequality includes both the positive and negative versions of the absolute value.

x<3 and x>−12

The solution is the set of values where x<3andx>−12.

−12<x<3

Answer 2

would it be d?

Answer 3

hello?

Answer 4

Sorry, all those -12's were suppose to be -1/2.

Answer 5

oh ok i was confused. Is the answer a?

Answer 6

Yes! Sorry, that was my bad. I was trying to type quickly.

Answer 7

Thank you

Answer 8

can you help me with another one?

Answer 9

Sure, I can try.