Solving Linear EquationsPart I

Presented by Mr. Laws

8th Math/Algebra 1

JCMS

Goal/Objective

8.EE.7 “Analyze and solve linear equations and pairs of simultaneous linear equations.

Essential Question

Using math principles, how can we find that a linear equations has a solution, many solutions, or no solution?

Using math principles, how do I identify properties that proves the equality of linear equations?

Properties of Equality

Addition Property of Equality

If the same number is added to both sides of an equation, the two sides remain equal. That is:If a = b, then a + c = b + cExample:a) 3 = 1+2; 3 + 2 = 1 + 2 + 2

Subtraction Property of Equality

If the same number is subtracted on both sides of an equation, the two sides remain equal. That is:If a = b, then a – c = b – c Example: 8 = 5 + 3; 8 – 2 = 5 + 3 – 2

Properties of Equality

Multiplication Property of Equality

If the same number is multiplied on both sides of an equation, the two sides remain equal. That is:

Division Property of Equality

If a real number is divided by the same number on both sides of an equation, the two sides remain equal.

That is:

If a = b, which c is not equal to zero: Then,

If a = b, then, a c b c

63

2 6

2 3 22

a b

c c

Example: 3 + 1 = 4, so

3 1 4

2 2

Solving Equations

To solve an equation containing a variable, you must find the value of the variable that will make the equation true. This is call the solution of the equation.

One way to solve an equation is to isolate the variable on one side of the equal sign.

By using the inverse operations, which are operations that undo one another. Addition, subtraction, multiplication, and division are inverse operations.

One Step Equations

Using the Addition Property of Equality

Solve: x – 10 = 2

x – 10 = 2

+ 10 + 10

x = 12

Step 1: Using Addition Property of Equality

One Step Equations

Using the Subtraction Property of Equality Solve y + 23 = 16

y + 23 = 16

- 23 - 23

y = -7

Step 1: Using the Subtraction Property of Equality

One Step Equations

Using the Multiplication Property of Equality Solve:

56

n

6 656

n

Step 1: multiply each side by 6 to isolate the variable on one side of the equal sign.

30n

6 is cross reduced in to 1 by dividing

One Step Equations

Using Reciprocals to Solve Equations. Solve: 3

94x

93 3

3

4

4 4x

Multiply each side by 4/3, which is the reciprocal of

¾.

12x

One Step Equations

Using the Division Property of Equality Solve 4c = -96

4 9

4 4

6c Step 1: Divide each side by 4

24c

Two Step Equations You can solve two steps equations using the properties of

equalities. For example:

3 6 18x -6 -6

3 12x 3 3

4x

2 4 36x +4 +4

2 40x 2 2

20x

Two Step Equations

13 9

6x

-3 -3

36x

2 88

a +2 +2

108

ax 86 8

80x

16

6x 6

In Summary

The Property of Equality provides you the principles to solve equations.

To find solution of equations you must find the value of the variable.

One way to solve equations is by using inverse operations to isolate the variable.

This is the basics for solving equations. Next we will move on to multiple step equations.

Make sure you take time to review and add any additional information about this lesson to your notes.