Section 2-1 Solve one-step Equations SPI 11B: identify the opposite of a rational number SPI 21E: Solve one and two step linear equations

Objectives: • Solve one-step linear equations using addition & subtraction

Opposite of a rational numbera number that is the same distance from zero on the number line but in the opposite direction

Solution of an equationValues that make an equation true

Equivalent equationsEquations that have the same solution

Addition Property of Equality: For every real number a, b, and c,

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

Properties of Equality – Used to Solve Equations

3 = (2 + 1) 3 + 4 = (2 + 1) + 4

Use the Addition Property of Equality (APE)

Solve the linear equation:

x - 4 = 6

Solve an equation: • isolate a variable on one side of the equal sign and put remaining terms on the other • what you do to one side of the equal sign, you must do to the other

x - 4 + 4= 6 + 4 Add 4 to both sides (APE)

x = 10 Simplify

Use the Addition Property of Equality (APE)

Solve the linear equation:

m – 3.24 = 5.2

Solve an equation: • isolate a variable on one side of the equal sign and put remaining terms on the other • what you do to one side of the equal sign, you must do to the other

m – 3.24 + 3.24 = 5.2 + 3.24 Add 3.24 to both sides (APE)

m = 16.848 Simplify

Properties of Equality – Used to Solve Equations

Subtraction Property of Equality: For every real number a, b, and c,

if a = b, then a - c = b – c.3 = (2 + 1) 3 - 2 = (2 + 1) - 2

Use the Subtraction Property of Equality (SPE)

Solve the linear equation:

x + 4 = 6

Solve an equation: • isolate a variable on one side of the equal sign and put remaining terms on the other • what you do to one side of the equal sign, you must do to the other

x + 4 - 4= 6 - 4 Sub 4 to both sides (SPE)

x = 2 Simplify

Use the Subtraction Property of Equality (SPE)

Solve the linear equation:

p + 4.1 = 5.32

Solve an equation: • isolate a variable on one side of the equal sign and put remaining terms on the other • what you do to one side of the equal sign, you must do to the other

p + 4.1 – 4.1 = 5.32 – 4.1 Sub 4.1 from both sides (SPE)

p = 1.22 Simplify

Inverse Operations

Inverse Operations: operations that undo one another

In the morning…. You go from home to school

Addition undoes Subtraction & Subtraction undoes Addition.

In the Evening…. You go from school to home

Start with 5 and add 3 to get 8

Subtract 3 from 8 to go back to 5

… the inverse would be …

Words and Linear Equations

Write and solve a linear equation for the following problem.

Josh earned $72. Mary and Josh together earned a total of $504.

How much money did Mary earn?

1. Define the unknown with a variable.m = Mary’s money

2. Write an equation using the variable to find the amount of money Mary earned.

m + 72 = 5043. Solve the equation using the Subtraction Property of Equality m + 72 – 72 = 504 - 72

m = 432

Mary earned a total of $432.

Real-World and Linear Equations

Together, you and your puppy weigh 128 lb.

If you alone weigh 115 lb, how much

does your puppy weigh?

1. Define the unknown with a variable.p = puppy’s weight

2. Write an equation using the variable to find the puppy’s weight

p + 115 = 1283. Solve the equation using the Subtraction Property of Equality p + 115 – 115 = 128 - 115

p = 13

The puppy weighs about 13 pounds

Find the value of a.

PQ = PR

11 = 6 + a The lengths of congruent sides are equal.

5 = a Simplify.

The value of a is 5.

11 – 6 = 6 + a – 6Subtract 6 from each side.

Check: 11 = 6 + a Check your solution in the original equation.11 6 + 5Substitute 5 for a.11 = 11

Geometry and Linear Equations