Question

solve the equation. 2x + 7 - 5x + 8 = 3(5 + 6x) - 12x use the sketch tool or paper if it helps with your thinking.

Explanation:

Step1: Combine like terms on left side

Combine the \(x\)-terms and constant terms on the left side of the equation. For the \(x\)-terms: \(2x - 5x=-3x\). For the constant terms: \(7 + 8 = 15\). So the left side becomes \(-3x+15\).

Step2: Expand right side

Use the distributive property \(a(b + c)=ab+ac\) on the right side. \(3(5 + 6x)=3\times5+3\times6x = 15+18x\). Then the right side of the equation is \(15 + 18x-12x\). Combine like terms on the right side: \(18x-12x = 6x\), so the right side is \(15+6x\).

Step3: Solve for \(x\)

Now our equation is \(-3x + 15=15+6x\). Subtract \(15\) from both sides: \(-3x+15 - 15=15+6x - 15\), which simplifies to \(-3x=6x\). Subtract \(6x\) from both sides: \(-3x-6x=6x - 6x\), so \(-9x = 0\). Divide both sides by \(-9\): \(x=\frac{0}{-9}=0\).

Answer:

\(x = 0\)