Question

1. solve the equation

$6x - 8(x - 2) = 20 + 2x$

Explanation:

Step1: Expand the left - hand side

Using the distributive property \(a(b - c)=ab - ac\), for \(-8(x - 2)\), we have \(-8\times x-(-8)\times2=-8x + 16\). So the original equation \(6x-8(x - 2)=20 + 2x\) becomes \(6x-8x + 16=20 + 2x\).

Step2: Combine like terms on the left - hand side

Combine \(6x\) and \(-8x\): \(6x-8x=-2x\). The equation is now \(-2x + 16=20 + 2x\).

Step3: Move the \(x\) terms to one side

Add \(2x\) to both sides of the equation: \(-2x+2x + 16=20 + 2x+2x\), which simplifies to \(16=20 + 4x\). Then subtract 20 from both sides: \(16-20=20-20 + 4x\), so \(-4 = 4x\).

Step4: Solve for \(x\)

Divide both sides of the equation \(-4 = 4x\) by 4: \(\frac{-4}{4}=\frac{4x}{4}\), which gives \(x=-1\).

Answer:

\(x = - 1\)