Question

solve the following equation.
$4x + 6 = 2(x + 5)$
$x = \square$ (simplify your answer.)

Explanation:

Step1: Expand the right side

Using the distributive property \(a(b + c)=ab+ac\), we expand \(2(x + 5)\) to get \(2x+10\). So the equation becomes \(4x + 6=2x + 10\).

Step2: Subtract \(2x\) from both sides

Subtract \(2x\) from both sides of the equation \(4x + 6=2x + 10\) to get \(4x-2x + 6=2x-2x + 10\), which simplifies to \(2x+6 = 10\).

Step3: Subtract 6 from both sides

Subtract 6 from both sides of the equation \(2x+6 = 10\) to get \(2x+6 - 6=10 - 6\), which simplifies to \(2x=4\).

Step4: Divide both sides by 2

Divide both sides of the equation \(2x=4\) by 2: \(\frac{2x}{2}=\frac{4}{2}\), which gives \(x = 2\).

Answer:

\(x = 2\)