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Mastering Equation Solving: Addition and Subtraction Strategies

This guide focuses on solving equations using addition and subtraction, key skills for algebraic manipulation. Learn to isolate variables through practical examples and applications. Understand the Addition and Subtraction Properties of Equality, which allow you to add or subtract the same number from both sides of an equation without altering its truth. From basic equations like x - 6 = 10 to trickier problems, this resource ensures you know how to verify your solutions effectively, enhancing your problem-solving abilities in real-world scenarios.

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Mastering Equation Solving: Addition and Subtraction Strategies

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  1. Solving Equations Using Addition and Subtraction (3.1) • A.4f Apply these skills to solve practical problems. • A.4b Justify steps used in solving equations. • Use a graphing calculator to check your solutions. Objectives:

  2. To Solve an Equation means... • To isolate the variable on one side of the equation. • Ex: x = 5 is solved for x. • y = 2x - 1 is solved for y.

  3. Addition Property of Equality For any numbers a, b, and c, if a = b, then a+ c= b+ c. What it means: You can add any number to BOTH sides of an equation and the equation will still hold true.

  4. An easy example: • Think about it… • Would you ever leave the house with only one shoe on? • Would you ever put blush on just one cheek? • Would you ever shave just one side of your face? • Would you ever add a number to just one side of an equation? • I hope you answered “No!” to all of these. We all know that 7 = 7. Does 7 + 4 = 7? NO! But 7 + 4 = 7 + 4. The equation is still true if we add 4 to both sides.

  5. Let’s try another example! x - 6 = 10 Add 6 to each side. x - 6 = 10 +6 +6 x = 16 Always check your solution!! The original problem is x - 6 = 10. Using the solution x=16, does 16 - 6 = 10? YES! 10 = 10 and our solution is correct.

  6. What if we see y + (-4) = 9? Recall that y+(-4)=9 is the same as y-4= 9. Now we can use the addition property. y - 4 = 9 +4 +4 y = 13 Check your solution! Does 13 - 4 = 9? YES! 9=9 and our solution is correct.

  7. How about -16 + z = 7? • Remember to always use the sign in front of the number. • 16 is negative, so we need to add 16 to both sides. • -16 + z = 7 +16 +16 z = 23 Check you solution! Does -16+23=7? YES! 7 = 7 and our solution is correct.

  8. A trick question... -n - 10 = 5 +10 +10 -n = 15 • Do we want -n? NO, we want positive n. • If the opposite of n is positive 15, then n must be negative 15. • Solution: n = -15 Check your solution! Does -(-15)-10=5? Remember, two negatives = a positive 15 - 10 = 5 so our solution is correct.

  9. Subtraction Property of Equality • For any numbers a, b, and c, if a = b, then a- c= b- c. What it means: • You can subtract any number from BOTH sides of an equation and the equation will still hold true.

  10. 3 Examples: 1) x + 3 = 17 -3 -3 x = 14 • Does 14 + 3 = 17? 2) 13 + y = 20 -13 -13 y = 7 • Does 13 + 7 = 20? 3) z - (-5) = -13 • Change this equation. z + 5 = -13 -5 -5 z = -18 • Does -18 -(-5) = -13? • -18 + 5 = -13 • -13 = -13 YES!

  11. Answer Now Solve x + 2 = -3To get the variable by itself, what is your first step? • Add 2 to both sides • Subtract 2 from both sides • Add 3 to both sides • Subtract 3 from both sides

  12. Answer Now Solve 8 = m - 3 • m = 5 • m = 11 • m = 24 • m = 8/3

  13. Answer Now Solve -y – (-3) = 7 • y = 10 • y = 4 • y = -10 • y = -4

  14. Try these on your own...

  15. The answers...

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