Question

1. solve the inequality $\frac{-8x + 20}{4}-10geq7$.
2. write the solution in set - builder notation.
3. graph the solution set.

Explanation:

Step1: Add 10 to both sides

$\frac{-8x + 20}{4}-10+10\geq7 + 10$
$\frac{-8x + 20}{4}\geq17$

Step2: Multiply both sides by 4

$4\times\frac{-8x + 20}{4}\geq17\times4$
$-8x + 20\geq68$

Step3: Subtract 20 from both sides

$-8x+20 - 20\geq68 - 20$
$-8x\geq48$

Step4: Divide both sides by -8 and reverse the inequality sign

$\frac{-8x}{-8}\leq\frac{48}{-8}$
$x\leq - 6$

Answer:

1. Set - builder notation: $\{x|x\leq - 6,x\in R\}$
2. To graph: Draw a closed - circle at $x = - 6$ (because the inequality includes equality, $x$ can be equal to - 6) and draw an arrow to the left to represent all real numbers less than or equal to - 6.