Question

problem 2: write a subtraction (-) inequality using the symbol ≤. a. solve the inequality. b. explain the process of solving the inequality c. draw the inequality on the number line d. write key words or phrases that match the symbol

Explanation:

Step1: Create a Subtraction Inequality

Let's create a subtraction inequality with $\leq$, e.g., $x - 3 \leq 5$.

Step2: Solve the Inequality

Add 3 to both sides: $x - 3 + 3 \leq 5 + 3$ → $x \leq 8$.

Step3: Explain the Process

To solve $x - 3 \leq 5$, we use the addition property of inequalities (adding the same number to both sides preserves the inequality). So, add 3 to both sides to isolate $x$, resulting in $x \leq 8$.

Step4: Draw on Number Line

• Draw a number line.
• Locate 8. Since the inequality is $\leq$, we use a closed dot at 8 (to include 8) and shade to the left (for all values less than or equal to 8).

Step5: Key Words/Phrases

Words/phrases for $\leq$: "at most", "no more than", "less than or equal to". For the subtraction part, "difference of", "subtracted from".

Answer:

(for part A solution):
The solution to the inequality \( x - 3 \leq 5 \) is \( \boldsymbol{x \leq 8} \).