Bell Quiz

Objectives Solve one-step equations by addition and subtraction.

New Concept An equation is a statement that uses an equal sign to show that two quantities are equal. A solution of an equation in on variable is a value of the variable that makes the equation true.

Example 1 Identifying Solutions State whether the value of the variable is a solution of the equation x + 6 = 9 for x = 3

Example 2 Identifying Solutions State whether the value of the variable is a solution of the equation x – 6 = 9 for x = 3

Lesson Practice State whether the value of the variable is a solution of the equation h – 14 = 2 for h = 12

Lesson Practice State whether the value of the variable is a solution of the equation –11 = j – 4 for j = – 7

Equivalent Equations An equation is like a balance scale. The scale remains balanced when the same quantity is added to both sides, or when the same quantity is subtracted from both sides. An equivalent equation has the same solution set.

Addition and Subtraction Properties of Equality By adding or subtracting the same quantity from both sides of an equation, each equation remains equivalent to the original equation Furthermore, each side of the equation remains balanced as the equation is solved. The Addition and Subtraction Properties of Equality hold for every real number a, b, and c.

Addition and Subtraction Properties of Equality Addition Property of Equality You can add the same number to both sides of an equation and the statement will still be true. Examples: 2 = 2 a = b = a + c = b + c 5 = 5 Subtraction Property of Equality You can subtract the same number from both sides of an equation and the statement will still be true. Examples: 10 = 10 a = b 10 – 4 = 10 – 4 a – c = b – c 6 = 6

Inverse Operations An inverse operation is an operation that undoes another. To solve an equation, isolate the variable on one side of the equal sign by using inverse operation Inverse Operations Addition Subtraction Multiplication Division

Example 3 Solving Equations by Adding Solve. Then check the solution. x – 3 = 12

Example 4 Solving Equations by Adding Solve. Then check the solution. –15 = n – 8

Lesson Practice Solve. Then check the solution. x – 5 = 17

Lesson Practice Solve. Then check the solution. – 30 = m – 12

Example 5 Solving Equations by Subtracting Solve. Then check the solution. k + 7 = 13

Example 6 Solving Equations by Subtracting Solve. Then check the solution. –21 = p + 9

Lesson Practice Solve. Then check the solution. p + 3 = 37

Lesson Practice Solve. Then check the solution. –14 = y + 8

Example 7 Solve Fraction Equations by Adding or Subtracting Solve. x – 3 8 =

Lesson Practice Solve. 1 d = 3 1 6

Example 8 Application: Weather On January 10, 1911, the temperature in Rapid City, South Dakota fell 47°F in 15 minutes. What was the temperature if it fell to 8°F?

Lesson Practice Sam took the same test twice. On the second test he scored 87, which was 13 points higher than on the first test. What was his first test score?