Question

m4|l5 solving any linear equation solve the equation. what is the value of u?
\\(\frac{1}{2}u + 2 = u + 6\\)
\\(\underline{ - \frac{1}{2}u \quad \quad \quad \quad - \frac{1}{2}u}\\)
\\(2 = \frac{1}{2}u + 6\\)
\\(\underline{ - 6 \quad \quad \quad \quad - 6}\\)
\\(-4 = \frac{1}{2}u\\)
multiply both sides by 2
multiply both sides by u
subtract 4 from both sides

Explanation:

Step1: Analyze the equation

We have \(-4 = \frac{1}{2}u\). To solve for \(u\), we need to isolate \(u\). The coefficient of \(u\) is \(\frac{1}{2}\), so we can multiply both sides by the reciprocal of \(\frac{1}{2}\), which is \(2\).

Step2: Multiply both sides by 2

Multiply both sides of \(-4=\frac{1}{2}u\) by \(2\):
\(2\times(-4)=2\times\frac{1}{2}u\)
Simplify both sides: \(-8 = u\) (since \(2\times\frac{1}{2}=1\), so \(1\times u = u\) and \(2\times(-4)= - 8\)).
Multiplying by \(u\) would complicate the equation (introduce \(u^{2}\)) and subtracting \(4\) doesn't help isolate \(u\), so multiplying by \(2\) is the correct step.

Answer:

Multiply both sides by 2