Solving Equations with
Variables on Both Sides
Warm Up
Lesson Presentation
Lesson Quiz

Solving Equations with
Variables on Both Sides
Warm Up
Simplify.
1. 4x – 10x
2. –7(x – 3)
–6x
–7x + 21
3.
2x + 3
4. 15 – (x – 2)
Solve.
5. 3x + 2 = 8
17 – x
2
6.
28
Holt McDougal Algebra 1

Solving Equations with
Variables on Both Sides
1) a=16
3) x = 0
5) r = 20
7) v =15
9) x = 9
11) v = -16
13) m = 5
15) n = 3
17) n = 11
21) n = 0
23) b = 12
Holt McDougal Algebra 1

Solving Equations with
Variables on Both Sides
• Notebook/Graph paper in front
• Dividers (in this order):
– Warm-Up/Closings
– Notes
– Classwork
– Homework
– Quiz/Test Review
– EOCT Review
Holt McDougal Algebra 1

Solving Equations with
Variables on Both Sides
Solve equations in one variable that contain variable terms on both sides.
Holt McDougal Algebra 1

Solving Equations with
Variables on Both Sides
To solve an equation with variables on both sides, use inverse operations to "collect" variable terms on one side of the equation.
Helpful Hint
Equations are often easier to solve when the variable has a positive coefficient. Keep this in mind when deciding on which side to "collect" variable terms.
Holt McDougal Algebra 1

Solving Equations with
Variables on Both Sides
Example 1: Solving Equations with Variables on Both Sides
Solve 7n – 2 = 5n + 6.
7n – 2 = 5n + 6
–5n –5n
2n – 2 = 6
+ 2 + 2
2n = 8
To collect the variable terms on one side, subtract 5n from both sides.
Since n is multiplied by 2, divide both sides by 2 to undo the multiplication.
n = 4
Holt McDougal Algebra 1

Solving Equations with
Variables on Both Sides
Check It Out!
Example 1a
Solve 4b + 2 = 3b.
4b + 2 = 3b
–3b –3b
b + 2 = 0
– 2 – 2
b = –2
To collect the variable terms on one side, subtract 3b from both sides.
Holt McDougal Algebra 1

Solving Equations with
Variables on Both Sides
Whiteboard Problem
Solve for x.
7x + 2 = 5x + 8
3
Holt McDougal Algebra 1

Solving Equations with
Variables on Both Sides
To solve more complicated equations, you may need to first simplify by using the Distributive
Property or combining like terms.
Holt McDougal Algebra 1

Solving Equations with
Variables on Both Sides
Example 2: Simplifying Each Side Before
Solving Equations
Solve 4 – 6a + 4a = –1 – 5(7 – 2a).
4 – 6a + 4a = –1 –5 (7 – 2a) Distribute –5 to the
4 – 6a + 4a = –1 –5 (7) –5 (–2a) expression in parentheses.
4 – 6a + 4a = –1 – 35 + 10a
4 – 2a = –36 + 10a
+36 +36
40 – 2a = 10a
+ 2a +2a
40 = 12a
Combine like terms.
Since –36 is added to 10a, add 36 to both sides.
To collect the variable terms on one side, add
2a to both sides.
Holt McDougal Algebra 1

Solving Equations with
Variables on Both Sides
Example 2 Continued
Solve 4 – 6a + 4a = –1 – 5(7 – 2a).
40 = 12a
Since a is multiplied by 12, divide both sides by 12.
Holt McDougal Algebra 1

Solving Equations with
Variables on Both Sides
Check It Out!
Example 2b
Solve 3x + 15 – 9 = 2(x + 2).
3x + 15 – 9 = 2 (x + 2) Distribute 2 to the expression
3x + 15 – 9 = 2 (x) + 2 (2) in parentheses.
3x + 15 – 9 = 2x + 4
3x + 6 = 2x + 4
–2x –2x
x + 6 = 4
– 6 – 6
x = –2
Combine like terms.
To collect the variable terms on one side, subtract 2x from both sides.
Since 6 is added to x, subtract
6 from both sides to undo the addition.
Holt McDougal Algebra 1

Solving Equations with
Variables on Both Sides
Whiteboard Problem
Solve for x.
4(2x – 5) = 5x + 4
8
Holt McDougal Algebra 1

Solving Equations with
Variables on Both Sides
Whiteboard Problem
Solve for a.
6 – 7(a + 1) = –3(2 – a)
Holt McDougal Algebra 1

Solving Equations with
Variables on Both Sides have your work checked before you may proceed.
• The problems you do not complete will be your homework for today.
Closing: Our first quiz will be on Friday. What will you do to prepare for it?
Holt McDougal Algebra 1