Solve the absolute value equation

What is the solution to the equation
|2x + 1| - 3 = 6

A.) x = -1 or 2
B.) x = -2 or 2
C.) x = -2 or 4
D.) x = -5 or 4

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First, isolate the absolute value to one side of the equation, while getting everything else to the other side.

|2x + 1| - 3 = 6
|2x + 1| = 9   {added 3 to each side}

Absolute value means “distance from zero”.
If the absolute value of 2x + 1 = 9, then that means (2x + 1) is 9 away from zero.
There are two numbers that are 9 away from zero......9 and -9. Therefore, 2x + 1 could be equal to 9 or -9.

|2x + 1| = 9
2x + 1 = 9 or 2x + 1 = -9   {set (2x + 1) equal to 9 and -9}
​2x = 8 or 2x = -10   {subtracted 1 from each side of each equation}
x = 4 or x = -5   {divided each side of each equation by 2}

D.) x = -5 or 4

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