Question

part a: write an addition inequality
x + 17 > 23
-17 -17 ← solve using subtraction
x > 6

part b: explain the process of solving the inequality

1. first, the operation shown is addition.
2. used its inverse, subtraction, by subtracting − 17 from both sides.
3. simplify to get x > 6

part c: graph the solution

number line from -10 to 10 with an open circle at 6 and arrow to the right

part d: write key words or phrases that match the inequality symbol

keywords for > are:

• greater than
• more than
• larger than

Explanation:

Step1: Analyze the inequality type

The inequality given is \(x + 17>23\), which is a linear inequality in one variable. The goal is to isolate \(x\).

Step2: Apply the inverse operation

To isolate \(x\), we use the inverse of addition (which is subtraction). Subtract 17 from both sides of the inequality: \(x + 17-17>23 - 17\).

Step3: Simplify both sides

Simplifying the left - hand side, \(x+17 - 17=x\). Simplifying the right - hand side, \(23-17 = 6\). So we get \(x>6\).

Answer:

To solve the inequality \(x + 17>23\):

1. Identify the operation on the variable side (addition of 17).
2. Use the inverse operation (subtraction) and subtract 17 from both sides: \(x+17 - 17>23 - 17\).
3. Simplify both sides to obtain the solution \(x>6\).