Writing Two-Step Inequalities Explained

This lesson covers writing and solving two-step inequalities, using algebra tiles for modeling, and applying these concepts to real-world problems. It also includes creating word problems from given inequalities, emphasizing the importance of understanding the direction of inequality signs when multiplying or dividing by negative numbers.

What is the first step in solving a two-step inequality?

• Graph the inequality

• Add or subtract a constant from both sides

• Multiply or divide both sides by a constant

• Combine like terms

When solving an inequality, what happens if you multiply or divide both sides by a negative number?

• The inequality sign changes direction

• The inequality sign is removed

• The inequality sign remains the same

• The inequality becomes an equation

In the mountain climbing example, what does the variable D represent?

• The target altitude

• The total altitude

• The number of days

• The average altitude gained each day

What is the inequality for the glee club trying to raise $6,000?

• 45x + 1240 = 6000

• 45x + 1240 > 6000

• 45x + 1240 ≤ 6000

• 45x + 1240 ≥ 6000

Ella has $40 to spend at the fair. If admission is $6 and each ride costs $3, what is the inequality to find the greatest number of rides she can go on?

• 6 + 3x ≤ 40

• 6 + 3x ≥ 40

• 6 + 3x < 40

• 6 + 3x > 40

What does 2x represent in the inequality 2x + 20 ≤ 50?

• The total distance run in two days

• The total number of days

• The total cost of two items

• The total number of items

Thomas has run 20 miles so far this week. If he intends to run 50 miles or less, how many miles should he run on each of the two remaining days?

• 20 miles

• 5 miles

• 10 miles

• 15 miles

Manny buys two work shirts each costing the same price. After using a $20 gift card, he can spend no more than $50. What is the maximum amount he could spend on each shirt?

• $10

• $15

• $20

• $25

Hank needs more than $30 to buy a video game. He already has $10 and earns $3 each time he cleans the dishes. How many times does he need to clean the dishes to earn enough to buy the game?

• 10 times

• 8 times

• 6 times

• 7 times

Henry buys five shirts after using a $50 gift card. He can spend no more than $100. What is the maximum amount he can spend on each shirt?

• $15

• $20

• $10

• $25