Question

4(3x - 8) < 6x + 4

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b - c)=ab - ac\), we get \(4\times3x-4\times8 = 12x - 32\). So the inequality becomes \(12x-32<6x + 4\).

Step2: Subtract \(6x\) from both sides

\(12x-6x-32<6x - 6x+4\), which simplifies to \(6x-32 < 4\).

Step3: Add 32 to both sides

\(6x-32 + 32<4 + 32\), resulting in \(6x<36\).

Step4: Divide both sides by 6

\(\frac{6x}{6}<\frac{36}{6}\), so \(x < 6\).

Answer:

\(x < 6\)