A student solves the following problem: 2(x - 2) + 5x = 24

Step 1: 2x - 4 + 5x = 24

Step 2: 10x - 4 = 24

Step 3: 10x - 4 + 4 = 24 + 4

Step 4: 10x = 28

Step 5: 10x/10=28/10

Step 6: x = 2.8

1 answer

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.