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### Solving Two-Step Inequalities

• A two-step inequality is an inequality that contains two operations such as addition and division or subtraction and multiplication.
• Solving two-step inequalities is very similar to solving two-step equations. Use inverse operations to isolate the variable. A difference is that in inequalities, when multiplying or dividing each side by a negative number, the inequality sign must be reversed.

## − 2x + 7 ≤ − 15. Solve for x.

• − 2x ≤ − 15 − 7
• − 2x ≤ − 22
• x ≤ − 22 ÷( − 2)

## [x/5] + 11 < 27. Solve for x.

• [x/5] < 27 − 11
• [x/5] < 16
• x < 16 ×5

## − 8x + 2 > 66. Solve for x.

• − 8x > 66 − 2
• − 8x > 64
• x < 64 ÷− 8

## − 2(9 + x) ≤ 24. Solve for x.

• 9 + x ≥ 24 ÷( − 2)
• 9 + x ≥ − 12
• x ≥ − 12 − 9

## [x/( − 0.1)] + 4 > 11. Solve for x.

• [x/( − 0.1)] > 11 − 4
• [x/( − 0.1)] > 7
• x < 7 ×( − 0.1)

## 9 − [x/4] < 49. Solve for x.

• − [x/4] < 49 − 9
• − [x/4] < 40
• x > 40 ×− 4

## 25x − 40 ≥ 10. Solve for x.

• 25x ≥ 10 + 40
• 25x ≥ 50

## 9 − 7x < 5. Solve for x.

• − 7x < 5 − 9
• − 7x < − 4
• x > − 4 ÷( − 7)

## Emily has \$ 55 to spend at the mall. She buys a pair of jeans for \$ 26 and sunglasses for \$ 15. Emily decides to spend the rest of her money on soft pretzels, which cost \$ 1.50 each. At most, how many pretzels can Emily buy?

• Let x = number of soft pretzels Emily can buy.
• \$ 26 + \$ 15 + \$ 1.50x ≤ \$ 55
• \$ 41 + \$ 1.50x ≤ \$ 55
• \$ 1.50x ≤ \$ 55 − \$ 41
• \$ 1.50x ≤ \$ 14
• x ≤ 9.3

## Daniel has \$ 23 to spend on school supplies. He needs to buy a book for English class and notebooks. The textbook costs \$ 18.75, and one notebook costs \$ 1.60. How many notebooks can Daniel buy?

• Let n = number of notebooks Daniel can buy.
• \$ 18.75 + \$ 1.60n ≤ \$ 23
• \$ 1.60n ≤ \$ 23 − \$ 18.75
• \$ 1.60n ≤ \$ 4.25
• n ≤ 2.66

## 0.6 − 2.8x ≤ 9[2/5]. Solve for x.

• − 2.8x ≤ 9[2/5] − 0.6
• − 2.8x ≤ [29/5] − [6/10]
• − 2.8x ≤ [29/5] − [3/5]
• − 2.8x ≤ [26/5]
• x ≥ [26/5] ×( − 2.8)
• x ≥ [26/5] ×( − 2[8/10])
• x ≥ [26/5] ×( − [28/10])
• x ≥ [26/5] ×( − [14/5])
• x ≥ − [364/25]

### x ≥ − 14.56

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.