Solving Equations
6x - 8 = 16
x = 4
7x - 9 = 3x + 15
x = 6
-4x - 7 > 13
x < -5
A movie theater charges $9 for a ticket and $4 for popcorn. If Mason spent $37 in total, how many popcorns did he buy if he purchased one ticket?
Equation: 4t + 9 = 37
Solution: t = 7
3(7x + 2) = 6
x = 0
4(2x + 3) = 52
x = 5
6x + 5 = 3x + 23
x = 6
-9x -7 ≥ 4x + 19
x ≤ -2 or -2 ≥ x
A gym membership costs a $25 joining fee plus $15 per month. If the total cost was $85, how many months has the member been enrolled?
Equation: 15m + 25 = 85
Solution: m = 4
4x + 12 = 4(x + 3)
Infinite Solutions
5(x + 2) - 7 = 18
x = 3
8x - 12 = 4x + 16
x = 7
2(3x + 5) ≤ 8x – 2
6 ≤ x or x ≥6
Jordan has at most $60 to spend. He wants to buy one sweatshirt for $20 and some bracelets that cost $3 each. Write and solve an inequality to find how many bracelets he can afford.
Equation: 3b + 20 ≤ 60
Solution: b ≤ 13.333
Rewritten: b ≤ 13
8x − 4 > 8x + 10
5(3x - 8) = -40
x = 0
2(4x + 3) = 5x + 21
x = 5
-2(5x – 9) < -32
x > 5
An amusement park charges $10 for entry and $4 per ride. If Alex has to spend less than $50, what is the greatest number of rides he can go on
Equation: 7r + 10 < 50
Solution: r < 5.714
Rewritten: r ≤ 5
A runner trains at a pace of 6.8 miles per hour. She wants to run more than 45 miles this week. Write an inequality to find out how many full hours she needs to run for.
Equation: 6.8 > 45
Solution: h > 6.617
Rewritten: h ≥ 7
3(x - 4) + 7 = 19
x = 8
5x + 9 = 15x – 10x - 9
6(x−2) +3x - 5 ≤ 9x–17
Infinite Solutions
For a school fundraiser, each T-shirt costs $8. The school spends $100 on materials. Write and solve an inequality to find how many shirts need to be sold to make at least $360 profit.
Equation: 8s - 100 ≥ 360
Solution: s ≥ 57.5
Rewritten: s ≥ 58
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