Question

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

Explanation:

Step1: Analyze operations on inequality

Starting with \(-5x - 3.5>6.5\), we should first add 3.5 to both sides, not subtract. Parul added when she should have subtracted, which is an error.

Step2: Analyze division of inequality

When dividing both sides of an inequality by a negative number (in this case - 5 when going from \(-5x>10\) to \(x > - 2\)), the inequality sign must be reversed. Parul did not change the \(>\) to \(<\).

Step3: Analyze number - line graphing

The solution of the correct inequality \(x<-2\) should use an open - circle on the number line since the inequality is strict (\(x
eq - 2\)). Parul used a closed circle instead.

Answer:

• She added 3.5 to both sides when she should have subtracted.
• She did not change the \(>\) symbol to a \(<\) symbol.
• She used a closed circle instead of an open circle on the number line.