Question

1. 2(3x - 1)

x 3
6x - 2
6x - 3x
3x
x

1. -\frac{2}{3}(x + 12)+\frac{2}{3}x=\frac{5}{4}x + 2

Explanation:

Step1: Expand the left - hand side

First, expand \(-\frac{2}{3}(x + 12)\) using the distributive property \(a(b + c)=ab+ac\). Here \(a =-\frac{2}{3}\), \(b=x\), \(c = 12\). So \(-\frac{2}{3}(x + 12)=-\frac{2}{3}x-8\). The original equation \(-\frac{2}{3}(x + 12)+\frac{2}{3}x=\frac{5}{4}x + 2\) becomes \(-\frac{2}{3}x-8+\frac{2}{3}x=\frac{5}{4}x + 2\).

Step2: Simplify the left - hand side

Combine like terms on the left - hand side. \(-\frac{2}{3}x+\frac{2}{3}x-8=-8\). So the equation is \(-8=\frac{5}{4}x + 2\).

Step3: Isolate the term with \(x\)

Subtract 2 from both sides of the equation. \(-8 - 2=\frac{5}{4}x+2 - 2\), which simplifies to \(-10=\frac{5}{4}x\).

Step4: Solve for \(x\)

Multiply both sides of the equation by \(\frac{4}{5}\) to solve for \(x\). \(x=-10\times\frac{4}{5}\). \(x=-8\).

Answer:

\(x=-8\)