Home > Algebra > Absolute Value Equations

How do you solve #abs(1/2x-3)=2#?

Answer 1

Genesis Allen

See explanation.

The equation with an absolute value must first be converted into a set of two equations without an absolute value.

is comparable to:

#1/2x-3=2 vv 1/2x-3=-2#

We can now resolve the two equations:

#1/2x=5 vv 1/2x=1#

#x=10 vv x=2 #

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Julia Adams

To solve the equation |(1/2)x - 3| = 2, first, isolate the absolute value expression on one side of the equation. Then, split the equation into two separate equations: one where the expression inside the absolute value bars is positive and one where it's negative. Solve both equations separately to find the possible values of x. In this case:

(1/2)x - 3 = 2
(1/2)x - 3 = -2
Add 3 to both sides: (1/2)x = 5
Multiply both sides by 2 to isolate x: x = 10
Add 3 to both sides: (1/2)x = 1
Multiply both sides by 2 to isolate x: x = 2

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.