Question

1. diego tried to solve the equation $\frac{1}{3}(x + 15) = 3$. what was his mistake?

$\frac{1}{3}(x + 15) = 3$
$\frac{1}{3}x = -12$
$x = -4$
word dividing by

Explanation:

Step1: Correct first step: eliminate fraction

Multiply both sides by 3:
$$3 \times \frac{1}{3}(x+15) = 3 \times 3$$
$$x + 15 = 9$$

Step2: Identify Diego's error

Diego incorrectly transformed $\frac{1}{3}(x+15)=3$ to $\frac{1}{3}x=-12$; he failed to distribute the $\frac{1}{3}$ to the 15, and incorrectly manipulated the constant term when moving 15 to the right.

Step3: Solve the correct equation

Subtract 15 from both sides:
$$x = 9 - 15$$
$$x = -6$$

Answer:

Diego made two key mistakes:

1. He did not properly distribute $\frac{1}{3}$ to both $x$ and 15 when starting to solve the equation.
2. He incorrectly rearranged the constants, leading to an wrong intermediate step $\frac{1}{3}x=-12$.

The correct solution for $x$ is $-6$.