The student made a mistake in Step 2. Let's go through the solution correctly to find the value of \( x \).
Starting with the original equation:
\[ 2(x - 2) + 5x = 24 \]
Step 1: Distribute the 2
\[ 2x - 4 + 5x = 24 \]
Step 2: Combine like terms
The terms \( 2x \) and \( 5x \) combine to give \( 7x \): \[ 7x - 4 = 24 \]
Step 3: Add 4 to both sides to isolate the term with \( x \)
\[ 7x - 4 + 4 = 24 + 4 \] \[ 7x = 28 \]
Step 4: Divide both sides by 7 to solve for \( x \)
\[ \frac{7x}{7} = \frac{28}{7} \] \[ x = 4 \]
So, the correct value of \( x \) is \( 4 \). The student calculated \( x = 2.8 \) due to an error in combining the terms in Step 2.