Algebra 1

Chapter 2 Section 1

2-1: Solving One-Step Equations

An equation is a mathematical statement that two expressions are equal.

A solution of an equation is a value of the variable that makes the equation true.

A solution set is the set of all solutions.

Finding the solution of an equation is also called solving the equation.

To solve an equation, we use inverse operations to isolate the variable.

Isolate means to get the variable alone on one side of the equation.

Inverse Operations

Add ↔ Subtract

Multiply ↔ Divide

Remember: What you do to one side of the equation you MUST do to the other side.

Addition Property of Equality: You can add the same number to both sides of an equation, and it will still be a true statement.

Subtraction Property of Equality: You can subtract the same number on both sides of an equation, and it will still be a true statement.

Multiplication Property of Equality: You can multiply both sides of an equation by the same number and it will still be a true statement.

Division Property of Equality: You can divide both sides of an equation by the same number and it will still be a true statement.

Example1: Solving Equations by Using Addition or Subtraction

Solve each equation.

A) x – 10 = 4

+10 +10

x = 14

Always look at the side of the equation where the variable is. Since the 10 is being subtracted, we will use the inverse operation, and add 10 to both sides.The 10s cancel, because +10 and – 10 equals 0. And 4 + 10 = 14.So, x is now isolated and x = 14.

B) 0.7 = r + 0.4

- 0.4 - 0.4

0.3 = r

r = 0.3

Look at the side with the variable.0.4 is being added, so we use the inverse operation, and subtract 0.4 from both sides.0.4 and – 0.4 equals 0 and cancels, and 0.7 – 0.4 = 0.3.So, 0.3 = r, we switch it around and say r = 0.3.

Now you try on the white board.

1) n – 3.2 = 5.6

2) -6 = k – 6

3) 6 + t = 14

Example 2: Solving Equations by Using Multiplication and Division

Solve each equation.

A) 13 = -2w

-2 -2

-13/2 = w

w = -13/2 = -6.5

Look at the side with the variable. When a number is written next to a variable it means multiplication.The inverse of multiplication is divide.So, divide by -2 on both sides.The -2s cancel because 2 divided by -2 equals 1.And -13/2 = w, or w = -13/2 or -6.5

B) -4 = k

-5

20 = k

k = 20

-5·

· -5 Look at the side with the variable.The operation is division.The inverse operation is multiplication. So, we multiply by -5 on both sides.The -5s cancel. -5 times -4 equals 20.So, 20 =k, k=20

Now you try on the white board.

4) P = 10

5

5) 0.5y = -10

6) C = 7

8

Example 3:

Solve each equation.

A) - 8 + b = 2

+8 +8

b = 10

Look at the side where the variable is. Even though the problem is +, we need to look at the sign on the 8. Since we want them to cancel, the opposite of -8 is +8. So, we + 8 on both sides. -8 and +8 equals 0, so they cancel.2 + 8 equals 10.So, b = 10.

B) 5/9v = 35

v = 639/5 ·

· 9/5 Look on the side with the variable.Since it is a fraction, we flip it over and multiply on both sides.9/5 and 5/9 cancel.35 times 9/5 = cancel the 5 into 35, 7 times, and 7 times 9 is 63.So, v = 63.

Now you try on the white board.

7) -2.3 + m = 7

8) -3 + z = 5

4 4

9) 1/6w =102