Solve Equations
Solve the equation.
y + 3.9 = 12.8
y = 8.9
Operations that "undo" each other are called ___________.
Inverse Operations
What is the difference between an expression and an equation?
An equation is a number sentence with an equal sign, an expression is a number sentence without an equal sign.
Leo’s soccer team purchased uniforms for $926.50. There are 17 athletes on the team. How much did each uniform cost? Define the variable then write an equation to describe the situation. Solve the equation, and check your solution.
x=cost of each uniform
17x = 926.50
x = $54.50
Check 17(54.50) = 926.50
Use substitution to determine which number is the given set is a solution of the equation.
{5, 6, 7, 8}
7/r + 1 = 2
Solve the equation.
-13b = 65
b = -5
Solve the equation.
15 = w + 4.75
10.25 = w
Solve the equation.
1/3(n) = 13
n = 39
Max and Kaiden went to the theater to watch Godzilla vs. Kong. Max bought a ticket for $10.75 and some popcorn. He paid $15.50 in total. How much was the popcorn? Define the variable and write an equation. Then solve the equation and check your solution.
p = cost of popcorn
10.75 + p = 15.50
p = 4.75
Solve the equation 4x = -116
x = -29
Solve the equation.
-8.5 = m - (-4.7)
m = -12.9
a/7 = -45.5
a = -318.5
Solve the equation. Write the solution as a mixed number if possible.
3/4(s) = -4/3
s = -1 7/9
Thomas had $43.85 in his piggy bank. He bought a new video game and now has $3.86 in his piggy bank. How much was the video game? Define the variable and write an equation. Then solve the equation and check your solution.
g=cost of the video game.
3.86 + g = 43.85
g=$39.99
Solve the equation.
x/-12 = -12
x = 144
Solve the equation.
x/-5.5 = -7
x = 38.5
The football team is losing the game in the fourth quarter. There are still 6,700 fans in attendance but 2,500 fans have already left. What was the total attendance at the game before the fans began to leave. Define the variable and write an equation. Then solve and check your solution.
x=attendance at the start of the game
x-2,500 = 6,700
x = 9,200
Solve the equation.
3/4(x) = 24
x = 18
Matthew wants to sell 30 items for a fundraiser. He knows that he as 5 days left to sell. Define the variable and write an equation to find how many items he must sell per day in order to reach his goal. Then solve the equation and check your solution.
x= number of items to sell each day
5x=30
x=6 items
Solve the equation.
-9.75x = 146.25
x = -15
Solve the equation.
3/5(x) = 5 1/2
x = 9 1/6
Devery is going on a rafting trip. She has rafted 12 3/4 miles and has 16 1/8 miles left to go. How many miles long is the trip? Define the variable and write an equation. Then solve and check your solution.
x=total miles of rafting trip
x - 12 3/4 = 16 1/8
x = 28 7/8
Solve the equation 7/10(x) = 3/4
x = 1 1/14
Alex and Elijah each bought popcorn at the movies. If they paid $13.50 total, how much did each boy pay? Define the variable and write an equation. Solve the equation and check your work.
x/2 = 13.50
x = $6.75
x/-8 = 40
x=-320