Question

solve 3(11 - 2x) = 2(-4x + 5)
options:
x = 6
x = 4.8
x = 3.5
x = 27

Explanation:

Step1: Expand both sides

Using the distributive property \(a(b + c)=ab+ac\), we expand the left - hand side \(3(1 - 2x)\) to get \(3\times1-3\times2x = 3-6x\), and the right - hand side \(2(-4x + 5)\) to get \(2\times(-4x)+2\times5=-8x + 10\). So the equation becomes \(3-6x=-8x + 10\).

Step2: Add \(8x\) to both sides

To get all the \(x\) terms on one side, we add \(8x\) to both sides of the equation \(3-6x=-8x + 10\). This gives us \(3-6x + 8x=-8x+10 + 8x\), which simplifies to \(3 + 2x=10\).

Step3: Subtract 3 from both sides

Subtract 3 from both sides of the equation \(3 + 2x=10\). We have \(3 + 2x-3=10 - 3\), which simplifies to \(2x=7\).

Step4: Divide both sides by 2

Divide both sides of the equation \(2x = 7\) by 2. So \(x=\frac{7}{2}=3.5\).

Answer:

\(x = 3.5\) (corresponding to the option \(x = 3.5\))