Solving and Graphing Inequalities with Variables on Both Sides

• x ≥ 2
• x ≥ -2
• x ≤ 2
• x ≤ -2

6(L+3) < 3(2L+6)

• L > 0

• L < 0 

• All real numbers

• No solution

• x ≤ 4
• x ≤ -4
• x ≥ 4
• x ≥ -4

• x ≥ 3
• x ≥ -3
• x ≤ 3
• x ≤ -3

• n ≤ 6
• n ≤ -6
• n ≥ 6
• n ≥ -6

• n < 1
• n < -1
• n > 1
• n > -1

The Rug store installs carpet for $80 plus $9.50 per square yard of carpet. The Magic Carpet charges $120 for installation and $7.50 per square yard of carpet. Write an inequality that could be used to determine the number of square yards of carpet that need to be installed for The Rug Store to charge more than The Magic Carpet.

• 80+9.50x > 120+7.50x

• 80+9.50x < 120+7.50x

• 80x+9.50 > 120x+7.50

• 80x+9.50 < 120x+7.50

Cody’s Gym charges a $15 fee to join and $30 per month. Tyler’s Gym charges a $30 fee to join and $20 per month. Write an inequality that could be used to determine after how many months Tyler’s gym would be a better deal.

• 30 + 20x < 15 + 30x

• 30x + 20 < 15x + 30

• 30 + 20x > 15 + 30x

• 30x + 20 > 15x + 30

Choose the situation that could represent the inequality:
25 – x < 15 + x

• Kasey has a gift card for $25. She buys a $15 CD and as many decals as she can buy with the rest of the gift card. How many decals can she buy?

• The school band has 25 people, and the theater class has 15 people. How many people must move from the band class to the theater class for the theater class to be as big or larger than the school band?

Mona is ordering cups for her school. Company A charges $3.50 for each cup and a one-time starter fee of $14. Company B charges $0.50 for each trophy and a one-time starter fee of $22. Which inequality can be used to find x, the minimum number of cups that can be ordereed so that the total charge at Company A is less than the total charge at Company B?

• 3.5x + < 0.5x + 22

• 3.5x + 14 > 0.5x + 22

• 3.5 + 14x < 0.5 + 22x

• 3.5 + 14x > 0.5 + 22x