Question

paul attempted to solve an inequality but made one or more errors. her work and the graph she drew are shown below. what errors did paul make? select three options. -5x - 3.5 > 6.5 -5x > 10 x > -50 she added 3.5 to both sides when she should have subtracted. she should have divided both sides by -5 as her first step. she divided one side by -5 while multiplying the other side by -5. she did not change the > symbol to a < symbol. she used a closed circle instead of an open circle on the number line.

Explanation:

Step1: Solve the inequality

Solve \(-5x - 3.5>6.5\).
First, add \(3.5\) to both sides: \(-5x-3.5 + 3.5>6.5 + 3.5\), which gives \(-5x>10\).
Then, divide both sides by \(-5\). When dividing an inequality by a negative number, the inequality sign flips. So \(x<- 2\).

Step2: Analyze each option

• Option 1: She added \(3.5\) to both sides when she should have subtracted.

This is incorrect. The correct first - step is to add \(3.5\) to both sides to isolate the term with \(x\) (\(-5x\)).

• Option 2: She should have divided both sides by \(-5\) as her first step.

This is incorrect. The first step is to get the term with \(x\) alone by adding \(3.5\) (not dividing by \(-5\) first).

• Option 3: She divided one side by \(-5\) while multiplying the other side by \(-5\).

This is incorrect. When solving \(-5x>10\), we divide both sides by \(-5\).

• Option 4: She did not change the \(>\) symbol to a \(<\) symbol.

This is correct. When dividing \(-5x>10\) by \(-5\), the inequality sign must flip.

• Option 5: She used a closed circle instead of an open circle on the number line.

Since \(x < - 2\) (not \(x\leqslant-2\)), the graph should have an open circle at \(-2\). This is correct.

Answer:

She did not change the \(>\) symbol to a \(<\) symbol; She used a closed circle instead of an open circle on the number line.