Question

solve: $7x + 4 \geq -17$ or $-6x + 5 \leq -7$

Explanation:

Step1: Solve \(7x + 4\geq - 17\)

Subtract 4 from both sides: \(7x+4 - 4\geq - 17 - 4\), which simplifies to \(7x\geq - 21\). Then divide both sides by 7: \(\frac{7x}{7}\geq\frac{-21}{7}\), so \(x\geq - 3\).

Step2: Solve \(-6x + 5\leq - 7\)

Subtract 5 from both sides: \(-6x+5 - 5\leq - 7 - 5\), which simplifies to \(-6x\leq - 12\). Divide both sides by - 6 (remember to reverse the inequality sign when dividing by a negative number): \(\frac{-6x}{-6}\geq\frac{-12}{-6}\), so \(x\geq 2\).

Step3: Combine the solutions

Since the inequality is "or", we take the union of the two solution sets. The solution to \(x\geq - 3\) or \(x\geq 2\) is \(x\geq - 3\) (because all numbers greater than or equal to 2 are also greater than or equal to - 3).

Answer:

\(x\geq - 3\)