Question

rachel solved the inequality below and graphed its solution set on the number line.

-3(x - 4) + x > 2

did rachel graph the solution set correctly, or did she make a mistake? explain with at least one complete sentence.

1. rodney solved the inequality below. his work is shown.

13x - 10 + 2x > 65
11x - 10 > 65
+ 10 + 10
11x > 75
11 11
x > 6.8

did rodney solve the inequality correctly? explain why or why not with at least one complete sentence.

Explanation:

Solve Rachel's inequality

Using the Solving Linear Inequalities knowledge point

$$
LATEXBLOCK0
$$

Analyze Rachel's graph

Using the Graphing Inequalities knowledge point

• The inequality is \(x < 5\).
• A correct graph needs an open circle at \(5\) pointing left.
• Rachel drew a closed circle at \(5\) pointing left.
• Rachel made a mistake by using a closed circle instead of an open circle.

Analyze Rodney's work

Using the Solving Linear Inequalities knowledge point

• Rodney's first step: \(13x - 10 + 2x > 65\) simplified to \(11x - 10 > 65\).
• He subtracted \(2x\) from \(13x\) instead of adding like terms: \(13x + 2x = 15x\).
• Rodney made a mistake in his first step by subtracting \(2x\) instead of adding it.

Answer:

Question 11

Rachel did not graph the solution set correctly because she used a closed circle at \(5\) instead of an open circle to represent the strict inequality \(x < 5\).

Question 12

Rodney did not solve the inequality correctly because he subtracted \(2x\) from \(13x\) to get \(11x\) in the first step instead of adding the like terms to get \(15x\).