Question

member methods for solving linear inequalities are similar to methods for solving linear equations. be sure to erse the direction of the inequality symbol when tiplying or dividing both sides of the inequality nbol by a negative number. b. $-8 + 2x = 2x - 8$ inequality. graph the solution set b. $7x - 2 \geq 30x - 48$

Explanation:

Step1: Solve the linear equation

Start with $-8 + 2x = 2x - 8$.
Subtract $2x$ from both sides:
$-8 + 2x - 2x = 2x - 8 - 2x$
Simplify to get $-8 = -8$

Step2: Solve the linear inequality

Start with $7x - 2 \geq 30x - 48$.
Subtract $7x$ from both sides:
$7x - 2 - 7x \geq 30x - 48 - 7x$
Simplify to $-2 \geq 23x - 48$

Step3: Isolate the term with x

Add 48 to both sides:
$-2 + 48 \geq 23x - 48 + 48$
Simplify to $46 \geq 23x$

Step4: Solve for x

Divide both sides by 23:
$\frac{46}{23} \geq \frac{23x}{23}$
Simplify to $2 \geq x$ or $x \leq 2$

Answer:

1. For the equation $-8 + 2x = 2x - 8$: All real numbers are solutions (the equation is an identity).
2. For the inequality $7x - 2 \geq 30x - 48$: $x \leq 2$

Graph for the inequality: Draw a closed circle at 2 on the number line, and shade all values to the left of 2.