Chapter 1 Lesson 5 (variables on both sides)

​Equations with variables on BOTH sides of the equal sign

​Chapter 1 Lesson 5

Steps for Solving Equations

1. Use Distributive Property if necessary.

2. Combine Like Terms

3. Move terms with variables to one side of the equal sign.

4. Move constants (without v​ariables) to the other side.

5. Get variable by itself. ​

Example:

3(2x + 4) + 2x = 4x -12​ (Distribute the 3)

6x + 12 + 2x = 4x -12 (Combine Like Terms)

​8x + 12 = 4x - 12 (Subtract 4x on both sides)

-4x -4x​

4x + 12 = -12 (Subtract ​12 on both sides)

-12 -12​

4x = -24​ (Divide by 4 on both sides)

​÷4 ÷4

x = -6​

Multiple Choice

Let's practice some more. What is the solution to this equation?

$$18\ -\ 2g\ =\ 4g$$  

• 3 = g

• g = 12

• 9 = g

• g = 16

Multiple Choice

$$3x\ +\ 5\ =\ 7x\ +\ 4$$  

• $$x\ =\ 4$$  

• $$x\ =\ -4$$  

• $$x\ =\ \frac{1}{4}$$  

• $$x\ =\ -\frac{1}{4}$$  

Multiple Choice

5 ( 3h - 9 ) - 12 = 12 - 7 ( h - 9 )

• h = 6

• h = 4

• h = 5

• h = 3

​Special Solutions

​Identity: an equation that is true for all values of the variable

​Equation has infinitely many solutions

​Special Solutions

​Some equations will not be true for any value of the variable

​Equation has no solution

Multiple Choice

Determine which one fits the expression

$$4\left(1-p\right)=-4p+4$$

• no solution

• infinitely many solutions

• one solution (aka regular equation)

Multiple Choice

Determine which one fits the expression

$$6m-m=\frac{5}{6}\left(6m-12\right)$$

• no solution

• infinitely many solutions

• one solution (aka regular equation)

Start here

Multiple Choice

The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride. Which equations could be used to determine how many rides you would need to go on for both fairs to be of equal value?

• 15x + 2.5 = 10x + 3

• 15 - 2.5x = 10 - 3x

• 15 + 2.5x = 10 + 3x

• 15 - 10 = 2.5x + 3x

Multiple Choice

A rental car agency charges $30.00 per day plus per mile $0.15. Another rental car agency charges $36.00 per day plus $0.10 per mile. How many miles would have to be driven in one day for both rental agencies to cost the same amount to rent? 

• 120 miles
• 100 miles
• 110 miles
• 150 miles 

Multiple Choice

Juan decided to join a gym to get in shape for football. He has two payment options. Option A is to buy a membership card and pay $2 each time he goes to the gym. Option B is to pay $4 each time he goes. A membership card costs $30. After how many times, t, will the cost of Option A be equal to the cost of Option B

• 50

• 20

• 15

• 25