Question

3(x - 4) - 9x ≥ 2x - 4

Explanation:

Step1: Expand the left - hand side

Using the distributive property \(a(b + c)=ab+ac\), for \(3(x - 4)\), we have \(3\times x-3\times4 = 3x-12\). So the inequality becomes \(3x - 12-9x\geq2x - 4\).

Step2: Combine like terms on the left - hand side

Combine \(3x\) and \(-9x\): \(3x-9x=-6x\). So the inequality is \(-6x - 12\geq2x - 4\).

Step3: Move all \(x\) terms to one side and constants to the other side

Add \(6x\) to both sides: \(-6x+6x - 12\geq2x + 6x-4\), which simplifies to \(-12\geq8x - 4\). Then add 4 to both sides: \(-12 + 4\geq8x-4 + 4\), so \(-8\geq8x\).

Step4: Solve for \(x\)

Divide both sides by 8: \(\frac{-8}{8}\geq\frac{8x}{8}\), which gives \(-1\geq x\) or \(x\leq - 1\).

Answer:

\(x\leq - 1\)