Solving by Combining Like Terms
5h + 2 + 2h = 23
h = 3
2(x + 5) = 14
x = 2
4x + 9 = 33
x = 6
WRITE AN EQUATION & SOLVE: Matt mows lawns and earns $50 per lawn. While mowing a customer's lawn, he received a $10 tip. Find the total number of lawns that Matt mowed last week if he made $210.
Let x = # of lawns
50x + 10 = 210
x = 4
Matt mowed 4 lawns last week.
The inverse of addition.
What is subtraction?
3b + b - 8 = 4
b = 3
5(d - 2) = 40
d = 10
x + 3x = -8
x = -2
Mr. Saler bought Hannah Montana t-shirts for a total of $90.93. Each of the 7 t-shirts cost the same amount. How many Hannah Montana t-shirts did Mr. Saler buy?
Let x = # of t-shirts
7n = 90.93 n = 12.99
Each t-shirt cost $12.99
The number of months in a year.
What is 12?
3a + 12 - 6a = -9
a = 7
7(x - 4) = -84
t = -8
4(y - 2) + y = -13
y = -1
Cary is a server in a restaurant. On a weekend night, she earned $4 an hour and $65 in tips. She made a total of $93. Write and solve an equation to determine how many hours she worked.
Let x = # of hours
4x + 65 = 93
x = 7
Carly worked 7 hours.
The number of inches in 1 foot.
What is 12?
-3y + 4 + 5y = -6
y = -5
-2(x - 9) = -24
x = 21
-6(m + 1) + 18 = 24
m = -2
Alisa bought tickets for her and her friends to go to the movies. Tickets cost $8 each and she also spends $19 on food. She spent a total of $51. Write and solve an equation to determine how many tickets Alisa bought.
Let x = # of tickets
8r + 19 = 51
r = 4
Alisa bought a ticket for herself and 3 other friends.
7 x 8
What is 56?
3c + 12 - c + 4 = 78
c = 31
-13(4 + 2a) = 208
a = -10
7k - 8 + 2(k + 12) = 52
k = 4
When you count by ones from many integers, you are counting consecutive integers. Using variables, three consecutive integers are n, n + 1, and n + 2. The sum of three consecutive integers is 48. What are the integers?
n + n + 1 + n + 2 = 48 n = 15 The integers are 15, 16, and 17.
0 divided by 34,896.
What is 0?