Solving Word Problems w/ Algebra

Algebra

To solve for a variable you must isolate the variable by using the “inverse” operation on both sides

(what do to one side you must do to the other)

Ask yourself “How do I make something zero”

You must make both sides of the equation equal.

Example: e + 3 = 14

e +3 -3 = 14 -3 (Inverse operation)

e = 11

Example

For an equation using addition, what is the inverse operation.

t + 4 = 17

t +4 -4 = 17 -4

t = 13

For equations using subtraction, what is the inverse operation?

u -8 = 2

U – 8 +8 = 2 + 8

Addition undoes subtraction, and subtraction undoes addition.

They are INVERSE operations

Isolate

To use inverse operations on both sides of an equation so the variable is by itself on one side

Operation Inverse Operation

Addition Subtraction

subtraction addition

Multiplication Division

Division Multiplication

Dani says that the equation j + 7 = 12 and 7 + j =12 cannot be solved the same way. What would

you say?

Example

Solve h- 25 = -11

Step 1: What is the operation of the equation?

Step 2: Inverse operation?

Step 3: Isolate

Step 4: Simplify

Solve d ◦ 11 = 99

What operation is being used?

12n =48

What is Order of Operations?

Two-Step Algebraic Equations

In two step equations, you will be doing 2 different inverse operations.

First, focus on the operations that does not involve the variable.

Example: 8v+5 = 13 8v +5 -5 =13 -5

Second, focus on the operation that is associated with the variable.

Example: 8v = 8

What is the inverse operation?

8v ÷ 8 = 8 ÷ 8 v = 1

Solve

5q -50 = 25

(g-8) / 5 = -13

s/4 + 3 = 9