Solving Two-Step Equations
NOTES
Class:______ Calc#:______
Notes # 15
Steps to solve equations:
GOAL: To get the variable by itself
Step 1: First you BOX the ______________________
Step 2: CANCEL what’s _________________________it
Add/Subtract using the inverse operation (opposite) to both sides
(if its add, you subtract…. You need OPPOSITE SIGNS to cancel)
Step 3: CANCEL what’s _____________________________ the box,
Multiply/Divide using the inverse operation (opposite) to both sides
(if its multiply, you divide – you need to use the SAME SIGN to cancel it!)
Step 4: _________________________! And you’ve Solved it!
***Remember: Equations must be balanced!!!!! (always do – ______________ SIDES!!!)
***Remember: You can always check your work!
Plug the solution back
into
equation.
Tell the two steps the
you
need to do after boxing the variable.
1. 2x + 3 = 9
2. 5 – 4x = -7
3. x - 8 = 6
Step 1:
Step 1:
Step 1:
Step 2:
Step 2:
Step 2:
Solve each equation below. Show all work to receive full credit.
ex1. 4y – 9 = 15
ex3. 35 = -2x - 15
1. 6x + 7 = -5
1
3
.
1
4
.
3. 10 - 6v = 4
1
3
.
1
4
.
ex2. -9t + 2 = 56
ex4. 12 – y = 30
2. -69 = 7v - 6
1
3
.
1
4
.
4. 10 – x = -12
1
3
.
1
4
.
Solving Two-Step Equations
NOTES
ex5.
1
t  6  7
2
5.1 12 
3
.
1
4
When you have a number.
in the denominator, first
multiply every term in the
equation by the number
in the denominator.
Then box and solve.
Class:______ Calc#:______
Notes # 15
1
x2
3
ex 7.
Write an equation and solve.
ex6. 3(2x + 5) = 39
x3
2
8
7.1
3
.
6.1 2(6x – 1) = -38
3
.
x
1
4
.
3
7
4
1
4
.
8. 331 students went on a field trip. Six buses were filled
and 7 students traveled in cars. How many students were
in each bus?
EQUATION:
SOLUTION: _______
9. Stephen is a pizza delivery driver. He earns $130 a week plus an
additional $0.75 for each delivery, d. How many pizzas did Stephen
deliver if he earned $178 before taxes last week.
EQUATION:
SOLUTION: _______
Solving Two-Step Equations
NOTES
Application
Class:______ Calc#:______
Notes # 15
Formulas for use with rectangles:
Area: __________
10. Find x
Perimeter: ________________
11. Find x
L = 4x
W= 5
12.
A = 60
Find x
L = 3x + 2
W= x + 4
13.
Find x
L = 5x
W= 4
r
P = 38
P = 28
L=5
W= 3
A=x–4
Solving Two-Step Equations
NOTES
Class:______ Calc#:______
Notes # 15
I. Complete each table using your graphing calculator.
[y=], type in equation, [2nd], [GRAPH]
1. y  2 x  1
x
-3
-1
0
2
2. y  3x  2
5
x
-3
y
y
-5
5
2
-7
II. Partner A____________________ Partner B_____________________ Solve each equation below.
Use the answer bank to check your answers.
A. 2x + 10 = -2
B. -9x + 1 = -80
A. 12 = -x – 5
B. -15 = -4x + 5
A.
10 – 6m = -104
B.
Answer Bank:
II.
Application
3
8n + 7 = 31
-17
10
𝐴 = 90
Write the equation and solve.
A. Aliyah had $24 to spend on seven
pencils. After buying them, she had
$10. How much did each pencil cost?
EQUATION:
SOLUTION:
-6
19
-243 = -9(10 + x)
9
Formulas for use with Rectangles: 𝐴 = 𝐿 ∙ 𝑊
For problems 10-11, find the value of x.
A.
𝐿 = 6𝑥
𝑊=3
A.
B.
5
3
B. 7(9 + x) = 84
17
𝑃 = 2𝐿 + 2𝑊
𝐿 = 2𝑥 + 5
𝑊 =𝑥+3
𝑃 = 40
B. Sumerlin bought a magazine for
$5 and four erasers. She spent a
total of $25. How much did each
eraser cost?
EQUATION:
SOLUTION: