Question

solve and graph the following inequality: 8 - 7x ≥ -10
inequality:
graph:

Explanation:

Step1: Isolate the term with x

Subtract 8 from both sides:

$$8 - 7x-8\geq - 10 - 8$$

$$ - 7x\geq - 18$$

Step2: Solve for x

Divide both sides by - 7. Remember to reverse the inequality sign when dividing by a negative number.

$$x\leq\frac{-18}{-7}=\frac{18}{7}$$

Answer:

The solution of the inequality is \(x\leq\frac{18}{7}\). To graph it, draw a number - line. Mark a closed circle at \(\frac{18}{7}\approx2.57\) (closed because the inequality includes equality, i.e., \(\geq\) was changed to \(\leq\) after dividing by a negative number) and shade the line to the left of \(\frac{18}{7}\).