Question

1. \\( -3x + 4 = -11 \\)

Explanation:

Identify the given equation and steps

The problem shows a handwritten solution for the equation:

$$-3x + 4 = -11$$

Let's analyze the steps shown in the image to find the errors.

Analyze the first step

Using the Two-Step Equations knowledge point, we isolate the variable term by subtracting \(4\) from both sides:

$$-3x + 4 - 4 = -11 - 4$$

$$-3x = -15$$

In the image, the student wrote \((-4)\) under both sides, but calculated:

$$-11 - 4 = 7$$

This is incorrect because \(-11 - 4 = -15\).

Analyze the second step

Using the Division Property of Equality knowledge point, we divide both sides by the coefficient of \(x\), which is \(-3\):

$$\frac{-3x}{-3} = \frac{-15}{-3}$$

$$x = 5$$

In the image, the student divided both sides by \(3\) instead of \(-3\):

$$\frac{-3x}{3} = \frac{7}{3}$$

This is incorrect because dividing by \(3\) leaves a negative sign with \(x\), and they also used the incorrect value \(7\) from the previous step.

Summarize the errors

1. Arithmetic Error: In the first step, subtracting \(4\) from \(-11\) should result in \(-15\), not \(7\).
2. Division Error: In the second step, to isolate \(x\), both sides must be divided by \(-3\) instead of \(3\).

Solve the equation correctly

Perform the correct operations:

$$-3x + 4 = -11$$

$$-3x = -15$$

$$x = \frac{-15}{-3}$$

$$x = 5$$

Answer:

The student made two errors in their work:

1. Subtraction Error: When subtracting \(4\) from both sides, they calculated \(-11 - 4\) as \(7\) instead of \(-15\).
2. Division Error: To isolate \(x\), they should have divided both sides by \(-3\) instead of \(3\).

The correct solution is:

$$-3x + 4 = -11$$

$$-3x = -15$$

$$x = 5$$