Solving Equations
Solve the following equation:
4 - 8x=13x + 2(2 + x)
x = 0
Solve the following equation:
(3/2)x = 14
x = 28/3
Solve the following inequality:
x + 15 > 27
x > 12
Henry put $3000 into a savings account that earns 6% simple interest each year. How much interest will he earn in one year?
Henry earns $180 in interest after one year.
Solve this problem by writing and solving an inequality. Define your variable.
Manny needs to buy 5 work shirts that are each the same price and a sweater for $20. He can spend no more than $70. What is the maximum amount that each shirt can cost?
x = cost of the shirt ($)
5x + 20 ≤ 70
Each shirt can cost at most $10.
Solve the following equation:
-(7 - 4x) = 9
x = 4
0.4x + 6 = 0.15x
x = -24
Solve the following inequality:
5x + 7 ≤ -23
x ≤ -6
Henry put $3000 into a savings account that earns 8% simple interest each year. How much money will he have altogether after one year?
Henry has $3240 altogether after one year.
Solve this problem by writing and solving an inequality. Define your variable.
Ricky has $18.00. Bagels cost $1.10 each and a small container of cream cheese costs $1.50. What is the greatest number of bagels Ricky can buy if he also buys one small container of cream cheese?
x = # of bagels Ricky can buy
1.1x + 1.5 ≤ 18
Ricky can buy a maximum of 15 bagels.
Solve the following equation:
3(5x - 2) - 6x = 3(3x + 2)
No Solution
Solve the following equation:
7x/4 - 3/2 = -5
x = -2
Solve the following inequality:
13 + 4x ≥ 3(x + 13)
x ≥ 26
There are 36 puppies at the dog park. This represents 8% of all of the dogs at the park. How many dogs are at the park?
There are 450 dogs at the park.
Solve this problem by writing and solving an inequality. Define your variable.
Jake has $50 to spend at Adventureland. He wants to get funnel cake while he is there, which costs $4 each. How many funnel cakes can Jake buy to still have at least $35 to spend on rides and games?
x = # of funnel cakes Jake can buy
4x + 35 ≤ 50
x ≤ 3.75
Jake can buy 3 funnel cakes.
Solve the following equation:
3(-3x + 4) = 15 - 11x + 2x - 3
Infinitely Many Solutions
Solve the following equation:
(4x - 3)/6 + 1/3 = x/2
x = 1
Solve the following inequality:
2(-8 - x) - 15 ≤ 9
x ≥ -20
The cost of a jacket increased from $75 to $81. What is the percent increase in the cost of the jacket?
The jacket increased by 8%.
Solve this problem by writing and solving an inequality. Define your variable.
The 35 members of a drill team are trying to raise at least $1,200 to cover travel costs to a training camp. They have already raised $500. How much money should each member raise to meet the goal?
x = amount of money each member should raise ($)
35x + 500 ≥ 1,200
Each member should raise at least $20.
Solve the following equation:
-5(1 - 5x) + 5(-8x - 2) = -4x - 8x
x = -5
Solve the following equation:
(-2x+1)/3 - (x+3)/7 = 8
x = -10
Solve the following inequality:
28 - x ≥ 7(x - 4)
x ≤ 7
Marty paid $72 for a jacket that had been discounted 20%. How much did the jacket cost before the discount?
The jacket cost $90 before the discount.
Solve this problem by writing and solving an inequality. Define your variable.
Molly saved $150 from her job to buy books. She goes to the store and buys books that cost $9.40 each. What is the maximum number of books Molly can buy to still have $9 left over to buy lunch?
x = # of books Molly buys
150 - 9.40x ≥ 9
Molly can buy a maximum of 15 books.