Question

1. error analysis describe and correct the error in solving $-\frac{1}{3}x + 2 = \frac{2}{3}x + 5$ by graphing.

the solution of
the equation
is 3.

Explanation:

Step1: Define the two linear functions

Let $y_1 = -\frac{1}{3}x + 2$ and $y_2 = \frac{2}{3}x + 5$. The solution to the equation is the $x$-value where $y_1=y_2$, i.e., the $x$-coordinate of the intersection point of the two lines.

Step2: Find intersection algebraically

Set $-\frac{1}{3}x + 2 = \frac{2}{3}x + 5$
Add $\frac{1}{3}x$ to both sides:
$2 = x + 5$
Subtract 5 from both sides:
$x = 2 - 5 = -3$

Step3: Identify the error

The original solution incorrectly used the $y$-coordinate of the intersection point instead of the $x$-coordinate as the solution to the equation.

Answer:

The error is that the solution was taken as the $y$-coordinate of the intersection point instead of the $x$-coordinate. The correct solution is $x=-3$.