Name: Absolute value equations: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 43 s
Description: What is the sum of the two solutions of the equation |2x - 3| = 7? Try it, then watch the animated solution.

Absolute value is distance from

0

. The equation says

2x - 3

is

7

units away from

0

.

Two numbers are

7

units from

0

:

7

and

{-7}

. So

2x - 3 = 7

or

2x - 3 = {-7}

.

First case: add

3

to both sides to get

2x = 10

, then divide by

2

:

x = 5

.

Second case: add

3

to both sides to get

2x = {-4}

, then divide by

2

:

x = {-2}

.

The question asks for the sum of the solutions:

5 + ({-2}) = 3

.

Traps:

5

is only one solution,

7

adds

5 + 2

and drops a negative,

0

uses

5

and

{-5}

.

Try it first