Question

5.5(2x + 1) = -5.5x + 63.25

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b + c)=ab+ac\), we expand \(5.5(2x + 1)\) to get \(5.5\times2x+5.5\times1 = 11x+5.5\). So the equation becomes \(11x + 5.5=- 5.5x+63.25\).

Step2: Add \(5.5x\) to both sides

To get all the \(x\) terms on one side, we add \(5.5x\) to both sides of the equation. \((11x + 5.5)+5.5x=(-5.5x + 63.25)+5.5x\). Combining like terms, we have \(11x+5.5x+5.5=-5.5x + 5.5x+63.25\), which simplifies to \(16.5x+5.5 = 63.25\).

Step3: Subtract 5.5 from both sides

Subtract \(5.5\) from both sides to isolate the term with \(x\). \((16.5x+5.5)-5.5=63.25 - 5.5\). This gives \(16.5x=57.75\).

Step4: Divide both sides by 16.5

Divide both sides of the equation by \(16.5\) to solve for \(x\). \(\frac{16.5x}{16.5}=\frac{57.75}{16.5}\). Calculating the right side, we find that \(x = 3.5\).

Answer:

\(x = 3.5\)