# Solving Addition and Subtraction 1 3 Equations Learn

Solving Addition and Subtraction 1 -3 Equations Learn to solve equations using addition and subtraction. Pre-Algebra

Solving Addition and Subtraction 1 -3 Equations An equation uses an equal sign to show that two expressions are equal. All of these are equations. 3 + 8 = 11 r + 6 = 14 24 = x – 7 100 = 50 2 To solve an equation, find the value of the variable that makes the equation true. This value of the variable is called the solution of the equation. Pre-Algebra

Solving Addition and Subtraction 1 -3 Equations Example 1: Determining Whether a Number is a Solution of an Equation Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Substitute each value for x in the equation. ? x + 8 = 15 ? 5 + 8 = 15 ? 13= 15 Substitute 5 for x. So 5 is not solution. Pre-Algebra

Solving Addition and Subtraction 1 -3 Equations Example 1 Continued Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Substitute each value for x in the equation. ? x + 8 = 15 ? 7 + 8 = 15 ? 15= 15 So 7 is a solution. Pre-Algebra Substitute 7 for x.

Solving Addition and Subtraction 1 -3 Equations Example 1 Continued Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Substitute each value for x in the equation. ? x + 8 = 15 ? 23 + 8 = 15 ? 31= 15 Substitute 23 for x. So 23 is not a solution. Pre-Algebra

Solving Addition and Subtraction 1 -3 Equations Addition and subtraction are inverse operations, which means they “undo” each other. To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign. Pre-Algebra

Solving Addition and Subtraction 1 -3 Equations To solve a subtraction equation, like y − 15 = 7, you would use the Addition Property of Equality. ADDITION PROPERTY OF EQUALITY Words You can add the same number to both sides of an equation, and the statement will still be true. Pre-Algebra Numbers Algebra 2+3=5 +4 +4 2+7=9 x=y x + z= y + z

Solving Addition and Subtraction 1 -3 Equations There is a similar property for solving addition equations, like x + 9 = 11. It is called the Subtraction Property of Equality. SUBTRACTION PROPERTY OF EQUALITY Words You can subtract the same number from both sides of an equation, and the statement will still be true. Pre-Algebra Numbers Algebra 4 + 7 = 11 − 3 4+4= 8 x=y x− z = y − z

Solving Addition and Subtraction 1 -3 Equations Example 2 A: Solving Equations Using Addition and Subtraction Properties Solve. A. 10 + n = 18 Subtract 10 from both sides. – 10 0+n= 8 Identity Property of Zero: 0 + n = n. n= 8 Check 10 + n = 18 ? 10 + 8 = 18 ? 18 = 18 Pre-Algebra

Solving Addition and Subtraction 1 -3 Equations Example 2 B: Solving Equations Using Addition and Subtraction Properties Solve. B. p – 8 = 9 p– 8=9 +8 +8 p + 0 = 17 p = 17 Check p– 8=9 ? 17 – 8 = 9 ? 9 = 9 Pre-Algebra Add 8 to both sides. Identity Property of Zero: p + 0 = p.

Solving Addition and Subtraction 1 -3 Equations Example 2 C: Solving Equations Using Addition and Subtraction Properties Solve. C. 22 = y – 11 + 11 Add 11 to both sides. 33 = y + 0 Identity Property of Zero: y + 0 = 0. 33 = y Check 22 = y – 11 ? 22 = 33 – 11 ? 22 = 22 Pre-Algebra

Solving Addition and Subtraction 1 -3 Equations Addition and subtraction are inverse operations, which means they “undo” each other. To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign. Pre-Algebra

Solving Addition and Subtraction 1 -3 Equations Try This: Example 1 Determine which value of x is a solution of the equation. x – 4 = 13; x = 9, 17, or 27 Substitute each value for x in the equation. ? x – 4 = 13 ? 9 – 4 = 13 ? 5= 13 Substitute 9 for x. So 9 is not a solution. Pre-Algebra

Solving Addition and Subtraction 1 -3 Equations Try This: Example 1 Continued Determine which value of x is a solution of the equation. x – 4 = 13; x = 9, 17, or 27 Substitute each value for x in the equation. ? x – 4 = 13 ? 17 – 4 = 13 ? 13 = 13 So 17 is a solution. Pre-Algebra Substitute 17 for x.

Solving Addition and Subtraction 1 -3 Equations Try This: Example 1 Continued Determine which value of x is a solution of the equation. x – 4 = 13; x = 9, 17, or 27 Substitute each value for x in the equation. ? x – 4 = 13 ? 27 – 4 = 13 Substitute 27 for x. ? 23 = 13 So 27 is not a solution. Pre-Algebra

Solving Addition and Subtraction 1 -3 Equations Try This: Example 2 A Solve. A. 15 + n = 29 – 15 0 + n = 14 Check 15 + n = 29 ? 10 + 14 = 29 ? 29 = 29 Pre-Algebra Subtract 15 from both sides. Identity Property of Zero: 0 + n = n.

Solving Addition and Subtraction 1 -3 Equations Try This: Example 2 B Solve. B. p – 6 = 7 p– 6=7 +6 +6 p + 0 = 13 p = 13 Check p– 6=7 ? 13 – 6 = 7 ? 7 = 7 Pre-Algebra Add 6 to both sides. Identity Property of Zero: p + 0 = p.

Solving Addition and Subtraction 1 -3 Equations Try This: Example 2 C Solve. C. 44 = y – 23 + 23 Add 23 to both sides. 67 = y + 0 Identity Property of Zero: y + 0 = 0. 67 = y Check 44 = y – 23 ? 44 = 67 – 23 ? 44 = 44 Pre-Algebra

Solving Addition and Subtraction 1 -3 Equations Example 3 A A. Thomas took a 34 -mile trip in his car, and the odometer showed 16, 550 miles at the end of the trip. What was the original odometer reading? odometer reading at the beginning of the trip + Solve: x miles traveled + x + 34 = 16, 550 – 34 x + 0 = 16, 516 x = 16, 516 34 = = odometer reading at the end of the trip 16, 550 Subtract 34 from both sides. The original odometer reading was 16, 516 miles. Pre-Algebra

Solving Addition and Subtraction 1 -3 Equations Example 3 B B. From 1980 to 2000, the population of a town increased from 895 residents to 1125 residents. What was the increase in population during that 20 -year period? initial population Solve: 895 + increase in population + 895 + n = 1125 – 895 0 + n = 230 n 1125 Subtract 895 from both sides. The increase in population was 230. Pre-Algebra = = population after increase

Solving Addition and Subtraction 1 -3 Equations Try This: Example 3 B B. From June to July, the water level in a lake has increased from 472 feet to 502 feet. What was the increase in water level during that 1 -month period? initial water level Solve: 472 + increase in water level + 472 + n = 502 – 472 0 + n = 30 n = = 502 Subtract 472 from both sides. The increase in water level was 30 feet. Pre-Algebra water level after increase

Solving Addition and Subtraction 1 -3 Equations An equation uses an equal sign to show that two expressions are equal. All of these are equations. 3 + 8 = 11 r + 6 = 14 24 = x – 7 100 = 50 2 To solve an equation, find the value of the variable that makes the equation true. This value of the variable is called the solution of the equation. Pre-Algebra

Solving Addition and Subtraction 1 -3 Equations Addition and subtraction are inverse operations, which means they “undo” each other. To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign. Pre-Algebra

Solving Addition and Subtraction 1 -3 Equations Example 2 A: Solving Equations Using Addition and Subtraction Properties Solve. A. 10 + n = 18 Subtract 10 from both sides. – 10 0+n= 8 Identity Property of Zero: 0 + n = n. n= 8 Check 10 + n = 18 ? 10 + 8 = 18 ? 18 = 18 Pre-Algebra

Solving Addition and Subtraction 1 -3 Equations Example 2 B: Solving Equations Using Addition and Subtraction Properties Solve. B. p – 8 = 9 p– 8=9 +8 +8 p + 0 = 17 p = 17 Check p– 8=9 ? 17 – 8 = 9 ? 9 = 9 Pre-Algebra Add 8 to both sides. Identity Property of Zero: p + 0 = p.

Solving Addition and Subtraction 1 -3 Equations Example 2 C: Solving Equations Using Addition and Subtraction Properties Solve. C. 22 = y – 11 + 11 Add 11 to both sides. 33 = y + 0 Identity Property of Zero: y + 0 = 0. 33 = y Check 22 = y – 11 ? 22 = 33 – 11 ? 22 = 22 Pre-Algebra

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