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Addition and Subtraction Equations: Solve for Unknown Variables

Learn how to solve addition and subtraction equations by applying inverse operations. Practice solving equations and word problems.

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Addition and Subtraction Equations: Solve for Unknown Variables

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  1. Transparency 2 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 2-3b Objective Solve addition and subtraction equations

  4. Example 2-3b Vocabulary Inverse operations Operations that “undo” each other

  5. Example 2-3b Review Vocabulary Solve Find a number that makes an equation true

  6. Lesson 2 Contents Example 1Solve an Addition Equation Example 2Solve a Subtraction Equation Example 3Use an Equation to Solve a Problem

  7. Example 2-1a Write the equation Ask “what is being done to the variable?” Solve The variable is being added by 14 Do the inverse operation on each side of the equal sign 14 14 - 14 14 - 14 + y = 20 14 - 14 + y = 20 - 14 Bring down the 14 Subtract 14 Bring down + y = 20 Subtract 14 1/3

  8. Example 2-1a Solve Combine “like” terms Bring down + y = Combine “like” terms 14 - 14 + y = 20 - 14 The Identify Property of Addition states that if you add 0 to any number, the number will not change 0 + y = 0 + y = 6 0 y y = 6 Bring down = 6 Answer: y = 6 1/3

  9. Example 2-1b Solve Answer: x = –10 1/3

  10. Solve Example 2-2a Write the equation Ask “what is being done to the variable?” The variable is being subtracted by 8 z - 8 z - 8 + 8 z - 8 + 8 = 12 z - 8 + 8 = 12 + 8 Do the inverse operation on each side of the equal sign Bring down the z - 8 Add 8 Bring down = 12 Add 8 2/3

  11. Solve Example 2-2a Bring down z Combine “like” terms Bring down = z - 8 + 8 = 12 + 8 Combine “like” terms The Identify Property of Addition states that if you add 0 to any number, the number will not change z z + 0 z + 0 = z + 0 = 20 z = 20 Bring down = 20 Answer: z = 20 2/3

  12. Solve Example 2-2b Answer: w = - 2 2/3

  13. Example 2-3a SPORTS If Tiger Woods had scores of –1, –4, and –3 on his first three rounds in a golf tournament, what would his fourth round score need to be if his final score was –18? Write an equation a + b + c + d = total In golf, they add the rounds to get the final score -1 + (-4) + (-3) -1 + (-4) + (-3) + d -1 + (-4) + (-3) + d = -18 Four rounds were played Replace first three rounds with scores given Fourth round is unknown Final score is total 3/3

  14. Example 2-3a SPORTS If Tiger Woods had scores of –1, –4, and –3 on his first three rounds in a golf tournament, what would his fourth round score need to be if his final score was –18? Combine “like” terms a + b + c + d = total Bring down + d = -18 -1 + (-4) + (-3) + d = -18 Ask “what is being done to the variable?” -8 -8 + d = -18 The variable is being subtracted by 8 Do the inverse operation on each side of the equal sign 3/3

  15. Example 2-3a SPORTS If Tiger Woods had scores of –1, –4, and –3 on his first three rounds in a golf tournament, what would his fourth round score need to be if his final score was –18? Do the inverse operation on each side of the equal sign a + b + c + d = total -1 + (-4) + (-3) + d = -18 Bring down the - 8 Add 8 -8 -8 + d = -18 Bring down the d = -18 -8 + 8 + d = -18 + 8 -8 -8 + 8 -8 + 8 + d = -18 -8 + 8 + d Add 8 3/3

  16. Example 2-3a SPORTS If Tiger Woods had scores of –1, –4, and –3 on his first three rounds in a golf tournament, what would his fourth round score need to be if his final score was –18? a + b + c + d = total Combine “like” terms -1 + (-4) + (-3) + d = -18 Bring down + d = -8 + d = -18 Combine “like” terms The Identify Property of Addition states that if you add 0 to any number, the number will not change -8 + 8 + d = -18 + 8 0 0 0 + d = 0 + d = -10 d d = -10 Bring down = -10 Answer: Tiger Woods needs to score –10 for the fourth round 3/3

  17. Example 2-3b * HIKING Kyle wants to hike a trail that is 7 miles long. If he hikes 2, 1, and 2 miles during the first three hours of his hike, how far would he need to hike in the fourth hour in order to complete the trail? Answer: 2 miles 3/3

  18. End of Lesson 2 Assignment

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