Solving Equations Using Addition and Subtraction

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Presentation transcript:

Solving Equations Using Addition and Subtraction Objectives: A.1 Solve linear equations in one variable. A.1 Apply these skills to solve practical problems. A.3 Justify steps used in solving equations.

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

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.

An easy example: We all know that 7 = 7. Does 7 + 4 = 7? NO! 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? 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.

Let’s try another example! 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. x - 6 = 10 Add 6 to each side. +6 +6 x = 16

What if we see y + (-4) = 9? Check your solution! Does 13 - 4 = 9? YES! 9=9 and our solution is correct. 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

How about -16 + z = 7? Remember to always use the sign in front of the number. Because 16 is negative, 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.

A trick question... Check your solution! Does -(-15)-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.

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.

3 Examples: 1) x + 3 = 17 3) z - (-5) = -13 -3 -3 -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!

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