Question

Solve and check the equation.
StartFraction 4 x Over 3 EndFraction minus 3 equals 13
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Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your answer.
A.
The solution set is StartSet nothing EndSet .
  
​(Type an integer or a simplified​ fraction.)
B.
The solution set is StartSet x vertical line x is a real number EndSet.
C.
The solution set is empty set.

Answer 1

Let's solve the equation step by step.

The given equation is:

\[
\frac{4x}{3} - 3 = 13
\]

**Step 1: Add 3 to both sides of the equation.**

\[
\frac{4x}{3} = 13 + 3
\]
\[
\frac{4x}{3} = 16
\]

**Step 2: Multiply both sides by 3 to eliminate the fraction.**

\[
4x = 16 \times 3
\]
\[
4x = 48
\]

**Step 3: Divide both sides by 4.**

\[
x = \frac{48}{4}
\]
\[
x = 12
\]

Now we found that \( x = 12 \).

**Step 4: Check the solution by substituting back into the original equation.**

Substituting \( x = 12 \) back into the original equation:
\[
\frac{4(12)}{3} - 3 = 13
\]
This simplifies to:
\[
\frac{48}{3} - 3 = 13
\]
\[
16 - 3 = 13
\]
\[
13 = 13
\]

The left side equals the right side, confirming our solution is correct.

**Part 1: Select the correct choice.**
The solution is \( x = 12 \).

So, the final answer is:
**C. The solution set is \(\{ 12 \}\).**