Question

Solve the equation. Check your answer.
22 equals 5 x plus 4 minus 3 x
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Part 1
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enter your response here ​(Simplify your​ answer.)

Answer 1

To solve the equation \( 22 = 5x + 4 - 3x \), we will first simplify the right side of the equation.

1. Combine like terms:
\[
5x - 3x = 2x
\]
Thus, the equation simplifies to:
\[
22 = 2x + 4
\]

2. Next, we will isolate the term with \( x \) by subtracting 4 from both sides:
\[
22 - 4 = 2x
\]
\[
18 = 2x
\]

3. Now, divide both sides by 2 to solve for \( x \):
\[
x = \frac{18}{2} = 9
\]

So, the solution is:
\[
x = 9
\]

**Check the answer:**

We will substitute \( x = 9 \) back into the original equation to verify:

Original equation:
\[
22 = 5x + 4 - 3x
\]

Substituting \( x = 9 \):
\[
22 = 5(9) + 4 - 3(9)
\]
Calculating each term:
\[
22 = 45 + 4 - 27
\]
Now simplify the right:
\[
22 = 45 + 4 = 49
\]
Then:
\[
49 - 27 = 22
\]

Since both sides of the equation are equal, our solution is confirmed to be correct.
Thus, the final answer is:
\[
\boxed{9}
\]