Unit 1: Review of Solving Linear Equations
1.1 Solving Multi-Step Equations
1.2 Distributive Property
Warm – up: Solve for the unknown variable
3x – 14 = 7
2(3x + 5) = 40
Solving Equations: Get the _________________ alone using ___________________ operations.
Ex 1:
Ex 3:
𝑥
4
+1=7
𝑥+3
2
=4
Ex 2:
3(𝑥 + 4) = 15
Ex 4:
4 − (5𝑥 + 8) = 11
Word-Problem: Samantha started a savings account with $100. She deposited the same amount of
money into the account twice a month. After 2 years, Samantha saved $2,500, how much money did
she deposit each time she visited the bank? Write an equation that models this situation and solve.
Unit 1: Review of Solving Linear Equations
1) t + 11 = 29
3
2)
x – 17 = 3
5
3) 2 a – 14 = 61
3
4)
9 = ¼(4 – 8x)
5) 3 – (3b + 1) = 8
6)
x – 4 = 14
2
7) Heather bought a winter coat for 6 less than half of its original price. She paid $65 for the
coat. What was the original price?
Unit 1: Review of Solving Linear Equations
1.3 Combining Like Terms
Ex 1)
-1 = 3x – 2x + 8
Practice
1.)
- 3x - 5 + 2x = -
5.)
7.)
5x – 6 + 4x = 48
4.)
-5x + 8 – 6x = - 36
6.)
-6 + 7x – 3x = -46
8.)
-7(9 – 3x) = -231
<b>answ er:</b
35 = 7x + 6x – 4
- 6 + 7x - 3x = -
2.)
<b>answ er:</b
- 4x – 6 – 4x = 50
- 5x + 8 - 6x = -
-3x – 5 + 2x = -14
<b>answ er:</b
7 = 9x + 4x + 7
5x - 6 + 4x = 48
3.)
Ex 2)
<b>answ er:</b
7(10 + x) = 14
Unit 1: Review of Solving Linear Equations
- 7(9 - 3x) = - 23
9.)
-5(3 + 5x) = -40
6( - 3x - 10) = - 1
11.)
15.)
17.)
12.)
- 6( - 3 – 7x) + 5(x – 3) = 186
14.)
-2(7 + 2x) = -50
16.)
5(3 + 2x) = 125
18.)
4(3 – x) = 4
<b>answ er:</b
6(3 + 5x) = 378
5(3 + 2x) = 125
6(-3x – 10) = -186
<b>answ er:</b
3(6x – 9) = -99
- 2(7 + 2x) = - 5
10.)
<b>answ er:</b
-7( -2 + 3x) = -175
- 6( - 3 - 7x) = 18
13.)
<b>answ er:</b
<b>answ er:</b
4(2x + 9) – 2(x + 6) = 33
Unit 1: Review of Solving Linear Equations
4(3 - x) = 4
19.)
<b>answ er:</b
-3(5x –10) = 45
3( - 5 + 4x) = 93
20.)
3(-5 + 4x) = 93
<b>answ er:</b
1.4 Equations with Variables on Both Sides of the Equal Sign
Ex 1: 2n – 9 = 7 - 2n
Ex 2: 8 – 3p = 2p – 7
Ex 3: The perimeter of a rectangle is 24 inches. Find the dimensions if the length is 3 inches longer
than the width.
Ex4: 6k – 3 = 4k + 2k + 13
Ex5: 5 + 2(k + 4) = 5(k – 3) + 10
Possible Solution Sets:
Practice
1.) 9t + 7 = 3t – 5
2.) 3n + 1 = 7n – 5
Unit 1: Review of Solving Linear Equations
3
1
t+4= t–6
7
7
3.) 8 – 2(t + 1) = -3t + 1
4.)
5.) 8x – 5(2 + x) = 2(x – 5) + x
6.) 4x – 9 = 7x + 12
7.) 8m + 13 = 13 + 8m
8.) 1.4f + 1.1 = 8.3 – f
9.) -3(b – 8) – 5 = 9(b + 2) + 1
10.) -4(2 – 3x) = 7 – 2(x – 3)
Unit 1: Review of Solving Linear Equations
1.5 Write each phrase as an algebraic expression
1.) 12 more than a number
2.) The quotient of a number and 9
3.) 4 times a number cubed decreased by 7
4.) The product of 5 and y added to 3
Translate each situation into an algebraic equation. THEN solve.
1) Ann has the 5 newest music CD’s which is 3 less than twice the amount that Bob has.
2) Mike, who has 6 video games, has half as many games as Paul.
3) Kate’s 85 on her English test was 37 points less than twice the grade on her Science test.
4) The 1,840 rock concert tickets sold were twice the amount of jazz concert tickets sold.
5) Meg received 90 votes for Student Council President, which were 50 less than twice the amount
that Tom received.
6) The 347 students who listed soccer as their favorite sport were 13 less than three times the
number of students who listed basketball as their favorite sport.
Unit 1: Review of Solving Linear Equations
1.6 Solving for Variables in Formulas
Solve for x in each of the following equations and formulas
Ex1) 2x – 4y = 7
Ex 2) 3ax – b = 7d
Ex 3) 4x – 3m = 2x – 5
Ex 4) x + 3ab = 4x + n
Ex 5) Solve for w in the formula for the perimeter of a Rectangle
P = 2l + 2w
Practice: Solve for x
1)
7x = t
2)
𝑥−𝑐
2
3)
ax – c = b
4)
5(2a + x) = 3b
=2
Unit 1: Review of Solving Linear Equations
Write an equation and solve the variable specified.
5) Five more than a number x is six less than twice a number y. Solve for x.
6) One-fourth of a number x is three more than three times a number y. Solve for x.
Review: Solve for x
1.
3.
5.
3x + 7 = -5
2.
-3(x + 5) = 3(x – 1)
4𝑥+5
7
=7
4.
y = mx – b
½ x + 4 = 2b
6.
3x – 2(x + 3) = x
Unit 1: Review of Solving Linear Equations
7.
A number divided by 3 is the same as 4 times the number minus 11.