Question

1. a student solved this equation: 3(2x - 5) = 7 - 3x

3(2x - 5) = 7 - 3x
6x - 5 = 4x
6x - 5 + 5 = 4x + 5
6x = 4x + 5
6x - 4x = 4x + 5 - 4x
2x = 5
x = 2.5
identify any errors the student made. correct the

Explanation:

Step1: Apply distributive property

The student made a mistake when distributing 3 in $3(2x - 5)$. It should be $3\times2x-3\times5 = 6x-15$, not $6x - 5$.
The correct first - step from $3(2x - 5)=7 - 3x$ is $6x-15 = 7-3x$.

Step2: Add $3x$ to both sides

$6x+3x-15=7-3x + 3x$
$9x-15 = 7$

Step3: Add 15 to both sides

$9x-15 + 15=7 + 15$
$9x=22$

Step4: Solve for $x$

$x=\frac{22}{9}\approx2.44$

Answer:

The student made a mistake in the distribution step. The correct solution is $x = \frac{22}{9}$.