How do you solve | 2x - 3 | = 5 ?

To solve the equation |2x - 3| = 5, you need to consider the definition of absolute value. This means that the expression inside the absolute value can equal either 5 or -5. Let's break it down into two separate equations.

Step 1: Set Up the Two Cases

We can write two equations based on the absolute value:

• Case 1: 2x - 3 = 5
• Case 2: 2x - 3 = -5

Solving Case 1

For the first case, solve for x:

• Add 3 to both sides: 2x = 5 + 3
• This simplifies to: 2x = 8
• Now, divide by 2: x = 4

Solving Case 2

Now, let's solve the second case:

• Add 3 to both sides: 2x = -5 + 3
• This simplifies to: 2x = -2
• Now, divide by 2: x = -1

Final Solutions

The solutions to the equation |2x - 3| = 5 are:

• x = 4
• x = -1

So, you have two values for x that satisfy the original equation!