Chapter 3.2 and Chapter 3.2 and 3.3 – Solving One-3.3 – Solving One-Step Equations 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 solutions of an equation is also called solving the equation.

Inverse Operations

Add x. Subtract x.

Multiply by x. Divide by x.

An equation is like a balanced scale. To keep the balance, you must perform the same inverse operation on both sides of the equation.

To find solutions, perform inverse operations until you have isolated the variable. A variable is isolated when it appears by itself on one side of an equation, and not at all on the other side.

Example 1 - Solve the equation and then check your solution.

Since 8 is subtracted from y, add 8 to both sides to undo the subtraction.

y – 8 = 24 + 8 + 8

y = 32

Check y – 8 = 24 32 – 8 24

24 24

To check your solution, substitute 32 for y in the original equation.

Example 2 - Solve the equation and then check your solution.

To check your solution, substitute 2.4 for t in the original equation.

Since 1.8 is added to t, subtract 1.8 from both sides to undo the addition.

4.2 = t + 1.8 –1.8 –1.8

2.4 = t

Check 4.2 = t + 1.84.2 2.4 + 1.84.2 4.2

Example 3 - Solve the equation. Check your answer.

Since 6 is subtracted from k, add 6 to both sides to undo the subtraction.

–6 = k – 6 + 6 + 6

0 = k

Check –6 = k – 6–6 0 – 6–6 –6

To check your solution, substitute 0 for k in the original equation.

Example 4 - Solve the equation. Check your answer.

Since v is multiplied by –6, divide both sides by –6 to undo the multiplication.

–24 = –6v

4 = v

Check –24 = –6v –24 –6(4)–24 –24

To check your solution, substitute 4 for v in the original equation.

-6 -6

Example 5 - Solve the equation. Check your answer.

Since j is divided by 3, multiply from both sides by 3 to undo the division.

–8 –8

To check your solution, substitute –24 for j in the original equation.

–24 = j

Check

Example 6 - Solve each equation. Check your answer.

Since y is multiplied by 0.5, divide both sides by 0.5 to undo the multiplication.

0.5y = –10

Check 0.5y = –10 0.5(–20) –10

–10 –10

To check your solution, substitute –20 for y in the original equation.

y = –20

Example 7 - Solve each equation. Then checkyour solution.

The reciprocal of is . Since w is multiplied by multiply both sides by .

20)24(65

Check : , , -20 = -20

w = 612

Example 8 - Solve the equation. Check your answer.

The reciprocal of is . Since w is multiplied by multiply both sides by .

Check

102 102

To check your solution, substitute 612 for w in the original equation.

Additional Example 9: Application

Ciro deposits of the money he earns from mowing lawns into a college education fund. This year Ciro added $285 to his college education fund. Write and solve an equation to find out how much money Ciro earned mowing lawns this year.

14

Additional Example 9 Continued

e = $1140

The original earnings were $1140 .

Write an equation to represent the relationship.

earnings is

times $285 14

14

41 e = 2854

1 The reciprocal of is . Since e is multiplied by , multiply both sides by

1414 4

1

41

.

e = $285

Tricky ProblemsSolve and check each equation

a.) f + (-14) = 10

b.) y – (– 1.3) = 2.4

c.) 915

3

a

x = 24

y = 1.1

a = 5

Chapter 3.2 and 3.3 Review…Solve and check each equation

1.) (– 3) + x = 10 2.) y – (–2.4) = 8.5

3.) – 7a = 56 4.) 832

x

x = 13 y = 6.1

a = -8 x = -12

Assignment• Worksheet 3-2 & 3-3 (Front & Back) (In-Class)• Page 132 #’s 15-35 (odd), 43-45 (all) (Homework)• Pages 138-139 #’s 13-31 (odd), 33-35 (all)

(Homework)

• (Make sure you WRITE out the problem and SHOW ALL YOUR WORK to receive full credit!!!)