1. 2.
x − 5 + 5 < 19 + 5 − 2x + 12 − 12 < −4 − − 12
3x < 24 −2x < -12
3x ÷ 3 < 24 ÷ 3 −2x ÷ -2 > -12 ÷ -2
x < 8 x > 6
3. Because you are not dividing or multiplying by a negative.
4. Because we divided by a negative, -2 in this case.
5. −7d + 8 > 29
-7d + 8 - 8 > 29 - 8
-7d > 21
-7d ÷ -7 > 21 ÷ -7
d < -3
6. 12 − 3b < 9
12 - 12 - 3b < 9 - 12
-3b < -3
-3b ÷ -3 < -3 ÷ -3
b > 1
7. z/7 - 6 ≥ 5
z/7 - 6 + 6 ≥ 5 + 6
z/7 x 7 ≥ 11 x 7
z ≥ 77
8. Fifty students are trying to raise at least $12,500 for a class trip. They have already raised $1,250. How much should each student raise, on average, in order to meet the goal? Write and solve the two step inequality for this problem.
An equation would be $1,250 + 50x = $12,500. To solve, subtract $1,250 from both sides of the equation. Next, divide both sides of the equation by 5. Each student should raise around $61.
9. At the end of the day, vegetables at Farm Market sell for $2.00 a pound, and a basket costs $3.50. If Charlene wants to buy a basket and spend no more than $10.00 total, how many pounds of vegetables can she buy? Write and solve the inequality.
An equation would be 2x + 3.50 ≤ 10. To solve, start by subtracting $3.50 from each side. Then, divide each side by two. She can by 3 and 1/4 pounds of fruit without going over her limit.
