Question

communicate your answer

1. how can you use division to solve an inequality?
2. use the rules you wrote in explorations 1(b) and 2(b) to solve each inequality.

a. $7x < -21$ b. $12 \leq 4x$ c. $10 < -5x$ d. $-3x \leq 0$

Explanation:

Step1: Solve \(7x < -21\)

Divide both sides by 7 (positive, inequality sign remains).
\(\frac{7x}{7} < \frac{-21}{7}\)
\(x < -3\)

Step2: Solve \(12 \leq 4x\)

Divide both sides by 4 (positive, inequality sign remains).
\(\frac{12}{4} \leq \frac{4x}{4}\)
\(3 \leq x\) or \(x \geq 3\)

Step3: Solve \(10 < -5x\)

Divide both sides by -5 (negative, reverse inequality sign).
\(\frac{10}{-5} > \frac{-5x}{-5}\)
\(-2 > x\) or \(x < -2\)

Step4: Solve \(-3x \leq 0\)

Divide both sides by -3 (negative, reverse inequality sign).
\(\frac{-3x}{-3} \geq \frac{0}{-3}\)
\(x \geq 0\)

Answer:

a. \(x < -3\)
b. \(x \geq 3\)
c. \(x < -2\)
d. \(x \geq 0\)