Question

1. 264 ≤ 8(3 - 7x) - 4x

Explanation:

Step1: Expand the right - hand side

First, we use the distributive property \(a(b + c)=ab+ac\) to expand \(8(3 - 7x)\). So \(8(3-7x)=8\times3-8\times7x = 24-56x\). Then the inequality \(264\leq8(3 - 7x)-4x\) becomes \(264\leq24-56x - 4x\).

Step2: Combine like terms

Combine the \(x\) - terms on the right - hand side. \(-56x-4x=-60x\), so the inequality is \(264\leq24 - 60x\).

Step3: Subtract 24 from both sides

Subtract 24 from both sides of the inequality: \(264 - 24\leq24-60x - 24\). Calculating the left - hand side, \(264 - 24 = 240\), and the right - hand side becomes \(-60x\). So we have \(240\leq-60x\).

Step4: Divide both sides by - 60 (and reverse the inequality sign)

When we divide both sides of an inequality by a negative number, the direction of the inequality sign changes. Divide both sides of \(240\leq-60x\) by \(-60\): \(\frac{240}{-60}\geq\frac{-60x}{-60}\). Calculating \(\frac{240}{-60}=-4\) and \(\frac{-60x}{-60}=x\). So we get \(x\leq - 4\).

Answer:

\(x\leq - 4\)