Question

simplify the following equations. write all answers using exact values.

1. $x = \frac{5 \pm 3}{2}$
2. $x = \frac{7 \pm 3}{4}$
3. $x = \frac{-5 \pm 1}{7}$
4. $x = \frac{-4 \pm 10}{4}$

Explanation:

Problem 5:

Step1: Calculate two cases for ±

First, when using the plus sign: $x = \frac{5 + 3}{2}$
Second, when using the minus sign: $x = \frac{5 - 3}{2}$

Step2: Simplify each fraction

For the plus case: $\frac{5 + 3}{2} = \frac{8}{2} = 4$
For the minus case: $\frac{5 - 3}{2} = \frac{2}{2} = 1$

Step1: Calculate two cases for ±

First, when using the plus sign: $x = \frac{7 + 3}{4}$
Second, when using the minus sign: $x = \frac{7 - 3}{4}$

Step2: Simplify each fraction

For the plus case: $\frac{7 + 3}{4} = \frac{10}{4} = \frac{5}{2}$
For the minus case: $\frac{7 - 3}{4} = \frac{4}{4} = 1$

Step1: Calculate two cases for ±

First, when using the plus sign: $x = \frac{-5 + 1}{7}$
Second, when using the minus sign: $x = \frac{-5 - 1}{7}$

Step2: Simplify each fraction

For the plus case: $\frac{-5 + 1}{7} = \frac{-4}{7}$
For the minus case: $\frac{-5 - 1}{7} = \frac{-6}{7}$

Answer:

$x = 4$ or $x = 1$

Problem 6: