Question

Solve for x. $|5x-75|>45-x$

• A. $x>7.5$
• B. $x>20$
• C. $x>7.5,x>20$
• D. $-20<x<-7.5$

Answer 1

The correct option is B $x>20$

We want to isolate the variable on one side & numbers on another side. Treat like a normal equation.
$|5x-75|>45-x$
We need to set-up two equations since it’s absolute value
$5x-75>45-x$ $-(5x-75)>45-x$
$6x>120$ $-5x+75>45-x$
$x>20$ $30>4x$
$7.5>x$
$x<7.5$
We must check each answer
Lets try 10
$|10\left(5\right)-75|>45-10$
25 > 35 this is not true. Therefore 7.5 > x is not true.
Lets try 30
$|5\left(30\right)-75|>45-30$
75 > 15 this is true. So, the correct answer is x > 20.