Modeling Equations
Error Analysis
Variables on both sides
Equations with Calculators
Equation Word Problems
100
Write an equation for this model.
-3x + 2 = x - 3
100
Below are the steps used to solve this equation
8x + 7 - 2x = 27 - 2
Step 1 6x + 7 = 25
Step 2 x + 7 = 19
Step 3 x = 12
Between which two steps was the mistake made?
Steps 1 and 2
100
8b = 22 - 3b
What is b?
b = 2
100
6r - 2 = r + 13
What is r?
r = 4
r = -6
r = 3
r = 2
r = 3
100
Write an equation for the following word problem.
The Space Club is having poster's printed. The printer charges $250 plus $2 per poster. How many posters can be printed for $1000.
250 + 2x = 1000
200
What is the value of x?
x = 2
200
What is the mistake? 
2x - 3x should be -1x, not 1x.
200
19x -5 = 10 + 24x
What is the value of x?
x = -3
200
3f - 4 = 2(3 - 1f)
What is f?
f = 2
f = -2
f = -8
f = 3
f = -2
200
Michael worked 40 hours last week. He had $74 deducted from his weekly earnings for taxes. If he had $286 left after the deduction, how much does Michael make per hour?
Write an equation
40x - 74 = 286
300
Write an equation for the model?
3x + 2 = x - 6
300
What is the mistake?
-27 divided by 3 should be -9
300
8x - 7 = 5(x-2)
x = -1
300
5(d - 2) = 40
What is d?
d = 10
d = 15
d = -10
d = 5
d = 10
300
Kimmy's car needed work. The mechanic charged her $140 for the parts and $48 for every hour of labor. If the bill totaled $260, how many hours of labor were required? **write an equation
140 + 48x = 260
400
Solve the model for x.
x = -4
400
Step 1: 6(a - 2) = -6 + 5a
Step 2: 6a - 12 = -6 + 5a
Step 3: a - 12 = -6
Step 4: a = 18
Between what two steps was the mistake made?
Between steps 3 and 4
400
6(2y + 5) = 4y + 30
What is the value of y?
y = 0
400
72 = 5(4x + 10) +2
Solve for x.
x = -1
x = -3
x = 4
x = 1
x = 1
400
You and your best friend both have savings account. Your savings account already has $120. You plan on taking $5 a week out for spending. Your friends saving account has $30. She plans on depositing $10 a week from babysitting. Write an equation to determine many weeks until you both have the same amount in your savings account.
120 - 5x = 30 + 10w
500
Draw a model for the following equation using the following key:
3x - 6 = -2x + 4
see boards
500
Step 1: 9t - 6 - 6t = 6
Step 2: 3t - 6 = 6
Step 3: 3t = 0
Step 4: t = 0
Between which two steps was a mistake made?
Between steps 2 and 3.
500
5(a - 4) = -2a + 8
What is the value of a?
a = 4
500
9(y - 4) - 7y = 5(3y - 2)
What is y?
y = -4
y = 2
y = -2
y = 7
y = -2
500
Acute Design charges a one time fee of $45 and then $11 for each shirt it prints. HiPeak Sportswear charges a one time fee of $75 and then $7 for each shirt it prints. Write an equation to show how many shirts would it take for the companies to charge the same amount?
45 +11x = 75 + 7x