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Example1

Title: Equations with absolute value

Grade 7+ Lesson s1-l1

Explanation: The best way to understand algebra is by looking at some examples. Take turns and read each example for easy understanding.

Examples

Topics → Definition Example1

Find the value of x if \$\∣ 2x − 1 \∣ = 9\$.

Step 1

Understanding Absolute Value The absolute value of a number represents its distance from zero on the number line.

Setting up Two Equations Since the absolute value of 2x - 1 is 9, there are two possibilities:

2x - 1 = 9 -→first
2x - 1 = - 9-→second

Solving the First Equation: 2x - 1 = 9

Add 1 to both sides: 2x = 10

Divide by 2: x = 5

Solving the Second Equation: 2x - 1 = -9

Add 1 to both sides: 2x = -8

Divide by 2: x = - 4

The solutions to the equation \$|2x - 1| = 9\$ are x = 5 and x = - 4.

Explanation:

The absolute value of an expression can be either positive or negative of the expression itself. So, \$| 2x - 1 | = 9\$ implies that 2x - 1 can be either 9 or -9. Solving both equations gives two possible values for x.