Chapter 3.2 and 3.3 – 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 solutions of an equation is also called solving 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. 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.

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. + 8 + 8 y = 32 Check y – 8 = 24 To check your solution, substitute 32 for y in the original equation. 32 – 8 24  24 24

Example 2 - Solve the equation and then check your solution. Since 1.8 is added to t, subtract 1.8 from both sides to undo the addition. –1.8 –1.8 2.4 = t Check 4.2 = t + 1.8 To check your solution, substitute 2.4 for t in the original equation. 4.2 2.4 + 1.8  4.2 4.2

–6 = k – 6 0 = k Example 3 - Solve the equation. Check your answer. + 6 + 6 Since 6 is subtracted from k, add 6 to both sides to undo the subtraction. 0 = k Check –6 = k – 6 To check your solution, substitute 0 for k in the original equation. –6 0 – 6 –6 –6 

4 = v Example 4 - Solve the equation. Check your answer. –24 = –6v Since v is multiplied by –6, divide both sides by –6 to undo the multiplication. -6 -6 4 = v Check –24 = –6v To check your solution, substitute 4 for v in the original equation. –24 –6(4) –24 –24 

Example 5 - Solve the equation. Check your answer. Since j is divided by 3, multiply from both sides by 3 to undo the division. –24 = j Check To check your solution, substitute –24 for j in the original equation.  –8 –8

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. y = –20 Check 0.5y = –10 To check your solution, substitute –20 for y in the original equation. 0.5(–20) –10 –10 –10 

Example 7 - Solve each equation. Then check your solution. The reciprocal of is . Since w is multiplied by multiply both sides by . 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 . w = 612 Check To check your solution, substitute 612 for w in the original equation. 102 102 

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. 1 4

Additional Example 9 Continued earnings is times $285 1 4  e = $285 Write an equation to represent the relationship. The reciprocal of is . Since e is multiplied by , multiply both sides by 1 4 . 1 4  e = 285 e = $1140 The original earnings were $1140 .

Solve and check each equation a.) f + (-14) = 10 Tricky Problems Solve and check each equation a.) f + (-14) = 10 b.) y – (– 1.3) = 2.4 c.) x = 24 y = 1.1 a = 5

Chapter 3. 2 and 3. 3 Review…Solve and check each equation 1 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.) x = 13 y = 6.1 a = -8 x = -12