Question

solve the equation please show the process to solve
4x+22=8x+10

Answer 1

To solve the equation \( 4x + 22 = 8x + 10 \), we can follow these steps:

1. **Get all terms involving \( x \) on one side of the equation**:
We can do this by subtracting \( 4x \) from both sides.

\[
4x + 22 - 4x = 8x + 10 - 4x
\]

This simplifies to:

\[
22 = 4x + 10
\]

2. **Get constant terms to the other side**:
Next, we will subtract \( 10 \) from both sides to get all the constant terms on the left side.

\[
22 - 10 = 4x + 10 - 10
\]

This simplifies to:

\[
12 = 4x
\]

3. **Solve for \( x \)**:
Now, divide both sides by \( 4 \) to isolate \( x \).

\[
x = \frac{12}{4}
\]

This simplifies to:

\[
x = 3
\]

Thus, the solution to the equation \( 4x + 22 = 8x + 10 \) is

\[
\boxed{3}
\]

### Verification:
To ensure that our solution is correct, we can substitute \( x = 3 \) back into the original equation.

Original equation:

\[
4x + 22 = 8x + 10
\]

Substituting \( x = 3 \):

\[
4(3) + 22 = 8(3) + 10
\]

Calculating both sides:

Left side:

\[
4 \times 3 + 22 = 12 + 22 = 34
\]

Right side:

\[
8 \times 3 + 10 = 24 + 10 = 34
\]

Since both sides are equal, the solution \( x = 3 \) is verified as correct.