Introduction to Solving Linear Equations

Introduction to Solving Linear Equations

Chapter Outline

8.1 Solve Equations Using the Subtraction and Addition Properties of Equality

8.2 Solve Equations Using the Division and Multiplication Properties of Equality

8.3 Solve Equations with Variables and Constants on Both Sides

8.4 Solve Equations with Fraction or Decimal Coefficients

Determine whether a number is a solution to an equation.

Step 1. Substitute the number for the variable in the equation.

Step 2. Simplify the expressions on both sides of the equation.

Step 3. Determine whether the resulting equation is true.

If it is true, the number is a solution.

If it is not true, the number is not a solution.

Subtraction and Addition Properties of Equality

Subtraction Property of Equality

For all real numbers a, b, and c,

if a = b then a−c=b−c.

Addition Property of Equality

For all real numbers a, b, and c,

if a = b then a+c=b+c.

Multiple Choice

Identify the property you would use to solve this equation:
y – 7 = 28

• Additive Property of Equality
• Subtraction Property of Equality
• Multiplicative Property of Equality
• Division Property of Equality

Determine whether each number is a solution to the equation.

3x+5=23.

ⓐ6

ⓑ235

In the following exercises, solve each equation.

n−18=31

9c=144

4y−8=16

−8x−15+9x−1=−21

−15a=120

x+3.8=8.2

10y=−5y+60

8n+2=6n+12

−5(2x+1)=45

Multiple Choice

What is the next step to solve this equation?
3x + 6 = 10 + 7x

• Add 6 to both sides of the equation

• Add 10 to both sides of the equation

• Add 7x to both sides of the equation

• Subtract 3x from both sides of the equation

Multiple Choice

What is the next step to solve this equation?
n - 4 = -2

• Add 4 to both sides of the equation

• Add n to both sides of the equation

• Subtract n from both sides of the equation

• Subtract 4 from both sides of the equation

Multiple Choice

What is the next step to solve this equation?
n - 4 = -2

• Add 4 to both sides of the equation

• Add n to both sides of the equation

• Subtract n from both sides of the equation

• Subtract 4 from both sides of the equation

Multiple Choice

What is the first step to solve this equation?
3n - 4 = -2 + 2n 

• Add 2n to both sides of the equation

• Add 3n to both sides of the equation

• Subtract 2n from both sides of the equation

• Subtract 4 from both sides of the equation

Multiple Choice

What is the next step to solve this equation?
3x - 5 = 7

• Add 5 to both sides of the equation

• Add 3x to both sides of the equation

• Subtract 5 from both sides of the equation

• Subtract 7 from both sides of the equation

Multiple Choice

3x - 5 = -26

• x=-21

• x=21

• x=-7

• x=61

Multiple Choice

19  + a  =  -50

• a = -950
• a =  -69
• a = -31
• a = -50/19

Multiple Choice

Solve the equation:
-5x = 25

• x = 20
• x = -20
• x = -5
• x = 5

Multiple Choice

A fitness club opens with 80 members. Each month the membership increases by 15 members. Which equation represents the relationship between the number of months the club has been opened, x, and the total fitness club membership, y?

• y=15x
• y=15x+80
• y=x+15
• y=80x+15

Multiple Choice

The local service center advertises that it charges a flat fee of $50 plus $8 per mile to tow a vehicle. Write an equation that represents the total cost (C) of a service for m miles of towing.

• y = 8x + 50

• C = 50m +8

• y = 50x + 8

• C = 8m + 50

Khan Academy

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:linear-equations-variables-both-sides/e/linear_equations_3