Solving One-Step Equations (2-2) Objective: Solve equations by using addition, subtraction, multiplication, and division.

Solve Equations Using Addition or Subtraction O In an equation, the variable represents the number that satisfies the equation. O To solve an equation means to find the value of the variable that makes the equation true. O The process of solving an equation involves isolating the variable (with a coefficient of 1) on one side of the equation. O Each step in this process results in equivalent equations. O Equivalent equations have the same solution.

Addition Property of Equality O If an equation is true and the same number is added to each side of the equation, the resulting equivalent equation is also true. O For any real numbers a, b, and c, if a = b, then a + c = b + c. 14 = = = = = 6

Example 1 O Solve by adding. O Horizontal Method: h – 12 = -27 h – = h = -15 O Vertical Method: h – 12 = h = -15 Check Your Solution: h – 12 = – 12 = = -27 

Solve Equations Using Addition or Subtraction O Similar to the Addition Property of Equality, the Subtraction Property of Equality can also be used to solve equations.

Subtraction Property of Equality O If an equation is true and the same number is subtracted from each side of the equation, the resulting equivalent equation is also true. O For any real numbers a, b, and c, if a = b, then a – c = b – c. 87 = – 17 = 87 – = = = -15

Example 2 O Solve by subtracting. O Horizontal Method: c = 36 c – 102 = 36 – 102 c = -66 O Vertical Method: c = c = -66 Check Your Solution: c = = = 36 

Solve Equations Using Multiplication or Division O In the equation x / 3 = 9, the variable x is divided by 3. O To solve for x, undo the division by multiplying each side by 3. O This is an example of the Multiplication Property of Equality.

Multiplication Property of Equality O If an equation is true and each side is multiplied by the same nonzero number, the resulting equation is equivalent. O For any real numbers a, b, and c, c ≠ 0, if a = b, then ac = bc. O If x = 5, then 3x = 15.

Division Property of Equality O If an equation is true and each side is divided by the same nonzero number, the resulting equation is equivalent. O For any real numbers a, b, and c, c ≠ 0, if a = b, then a / c = b / c. O If x = -20, then x / 5 = -20 / 5 or -4. O The reciprocal of a number can be used to solve equations.

Example 3 O Solve each equation. -75 = -15b = b b = 5 4 x = 32

Example 4 O We can also use reciprocals and properties of equality to solve real-world problems. O Ricardo is driving 780 miles to Memphis. He drove about 3 / 5 of the distance on the first day. About how many miles did Ricardo drive? m = 468 miles

Check Your Progress O Choose the best answer for the following. O Water flows through a hose at a rate of 5 gallons per minute. How many hours will it take to fill a 2400-gallon swimming pool? A. 4 h B. 6 h C. 8 h D. 16 h m = 480 minutes ÷ 60

Check Your Progress O Choose the best answer for the following. O Solve a – 24 = 16. Then check your solution. A. 40 B. -8 C. 8 D. -40 a – 24 = a = 40 a – 24 = – 24 = = 16 

Check Your Progress O Choose the best answer for the following. O Solve k = -42. Then check your solution. A. 87 B C. 171 D k = k = k = (-171) = = -42 

Check Your Progress O Choose the best answer for the following. O Solve A.. B.. C.. D. 5

Check Your Progress O Choose the best answer for the following. O Solve 32 = -14c. A. -3 B. 46 C. 18 D.. 32 = -14c -14