Question

1. solve the equation for the value of m.

m + 6 = m - 4

1. solve the equation for the value of x.

8x + 3 = 3(2x + 5)

1. solve the equation for the value of x.

\frac{1}{2}(6x - 10)+2x = 25

Explanation:

Step1: Expand the equation

\[

$$\begin{align*} 8x + 3&=3(2x + 5)\\ 8x+3&=6x + 15 \end{align*}$$

\]

Step2: Move like - terms to one side

Subtract \(6x\) from both sides: \(8x-6x + 3=6x-6x + 15\), which simplifies to \(2x+3 = 15\). Then subtract 3 from both sides: \(2x+3 - 3=15 - 3\), getting \(2x=12\).

Step3: Solve for \(x\)

Divide both sides by 2: \(\frac{2x}{2}=\frac{12}{2}\), so \(x = 6\).

for the second - part:

Step1: Distribute the fraction

\[

$$\begin{align*} \frac{1}{2}(6x - 10)+2x&=25\\ 3x-5 + 2x&=25 \end{align*}$$

\]

Step2: Combine like - terms

\((3x+2x)-5 = 25\), which gives \(5x-5 = 25\).

Step3: Isolate the variable term

Add 5 to both sides: \(5x-5 + 5=25 + 5\), resulting in \(5x=30\).

Step4: Solve for \(x\)

Divide both sides by 5: \(\frac{5x}{5}=\frac{30}{5}\), so \(x = 6\).

Answer:

\(x = 6\)