Question

Given: 6|x/3| < 18

Part A: Show the step(s) to get the absolute value expression by itself.

Part B: Write the two equations used to solve the absolute value equation.

Part C: Solve the equations and check your equations.

Answer 1

see below

Explanation:

6|x/3| < 18

Divide by 6

6/6|x/3| < 18/6

|x/3| < 3

Now we get two equations, one positive and one negative, remembering to flip the inequality

x/3 < 3 x/3 > -3

Multiply by 3 to isolate x

x/3 *3 < 3*3 and x/3*3 > -3*3

x < 9 and x > -9

Rewriting

-9 < x<9

Check -12

6|-12/3| < 18

6|-4| <18

24<18 False good

Check 0

0<18 true

Check 12

6|12/3| < 18

6|4| <18

24<18 False good