One Step Equations

Solving Equations usingAddition and Subtraction

Algebra Seminar2012-2013

How to Solve an Equation

Think of equations as a balance of two things.

The left side and right side of the equation must be equal.

Whatever you do to one side has to be done to the other to keep it balanced!

Our goal = To make both sides of the equation equal!

* A variable is a letter which represents an unknown number. Any letter can be used as a variable.

* An algebraic expression contains at least one variable.

Examples: a, x+5, 3y – 2z

* A verbal expression uses words to translate algebraic expressions.

Example: “The sum of a number and 3” represents “n+3.”

* An equation is a sentence that states that two mathematical expressions are equal.

Example: 2x-16=18

Vocabulary

Steps to Solving Equations

1. Simplify each side of the equation, if needed, by distributing or combining like terms.

2. Move variables to one side of the equation by using the opposite operation of addition or subtraction.

3. Isolate the variable by applying the opposite operation to each side.

• First, use the opposite operation of addition or subtraction.

• Second, use the opposite operation of multiplication or division.

4. Check your answer.

When we solve an equation, we will use “opposite

operations”.Addition/Subtraction

x + 8 = 2-8 -8

x = -6

y - 13 = -4+13 +13

y = 9

When solving equations, we want to simplify the equation to make it as

easy as possible.

y + (-3) = 8 is rewritten as y – 3 = 8

p – (-5) = 6 is rewritten asp + 5 = 6

As a general rule, replace “+ (- )” with “–” and “– (- )” with “+ ”. This will make things less confusing in the

future!

1) Solve r + 16 = -7To solve, you must get the variable by

itself. What number is on the same side as r?

16To get r by itself, we must undo the

“add 16”. What is the opposite of addition?

Subtract 16

When we subtract 16 on both sides we know that r = -23!

Solve. w + 14 = -8

Solve.y + (-10) = 6

Solve.-11 = a + 8

Solve.-13 + h = -5

Solve.-7 = -16 - k

Solve.m - (-13) = 37

Solve.z + (-13) = -27

Solve.p - (-27) = 13

Solve.41 = 32 + r

Solve.d + 16 = 14

Solve.x + 15 = -6

Sarah heard on the morning news that the temperature had dropped 26 degrees since midnight. In the morning, the temperature

was –8°F. What was the temperature at midnight?

To solve this problem we should Make a Plan and Write an Equation.

Let t be our variable to represent the temperature at midnight and use the equation

model, so t – 26 = -8.

If we add 26 to both sides, we see that the temperature at midnight was 18 degrees!

Real World Equations