7th grade math quiz: Graphing two-step inequalities

📚 Quick Study Guide

🔢 Isolating the Variable: The goal is to get the variable alone on one side of the inequality. Use inverse operations to undo addition, subtraction, multiplication, or division. Remember to perform the same operation on both sides. ⚖️ Addition/Subtraction Property: Adding or subtracting the same number from both sides of an inequality does not change the inequality. ➗ Multiplication/Division Property: Multiplying or dividing both sides of an inequality by a positive number does not change the inequality. However, multiplying or dividing by a negative number *reverses* the inequality sign. 📈 Graphing on a Number Line:
⏺️ Use an open circle (o) for inequalities with < or > (not included). ◼️ Use a closed circle (●) for inequalities with $\leq$ or $\geq$ (included). ➡️ Shade to the right for greater than (>) or greater than or equal to ($\geq$). ⬅️ Shade to the left for less than (<) or less than or equal to ($\leq$).

🧪 Practice Quiz

1. What is the first step in solving the inequality $2x + 3 > 7$?
1. Add 3 to both sides.
2. Subtract 3 from both sides.
3. Divide both sides by 2.
4. Multiply both sides by 2.
2. Solve the inequality $3x - 5 \leq 4$.
1. $x \leq 3$
2. $x \geq 3$
3. $x \leq -3$
4. $x \geq -3$
3. What type of circle is used on the number line when graphing $x < 5$?
1. Closed circle
2. Open circle
3. Dotted circle
4. Triangle
4. Solve for x: $-2x + 1 \geq 9$
1. $x \geq -4$
2. $x \leq -4$
3. $x \geq 5$
4. $x \leq 5$
5. Which inequality is represented by a closed circle at -1 and shading to the left?
1. $x > -1$
2. $x < -1$
3. $x \geq -1$
4. $x \leq -1$
6. Solve: $\frac{x}{4} - 2 > -1$
1. $x > 4$
2. $x < 4$
3. $x > -4$
4. $x < -4$
7. What is the solution to $5 - x \leq 8$?
1. $x \geq -3$
2. $x \leq -3$
3. $x \geq 3$
4. $x \leq 3$