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Published byDarlene Bailey Modified over 9 years ago
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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 :
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To isolate the variable on one side of the equation. Ex: x = 5 is solved for x. y = 2x - 1 is solved for y.
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For any numbers a, b, and c, if a = b, then ac = bc. What it means: You can multiply BOTH sides of an equation by any number and the equation will still hold true.
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We all know that 3 = 3. Does 3(4) = 3? NO! But 3(4) = 3(4). The equation is still true if we multiply both sides by 4. Would you ever put deodorant under just one arm? Would you ever put nail polish on just one hand? Would you ever wear just one sock?
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Always check your solution!! The original problem is x = 4 2 Using the solution x = 8, Does 8/2 = 4? YES! 4 = 4 and our solution is correct. x = 4 2 Multiply each side by 2. (2)x = 4(2) 2 x = 8
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Division Property of Equality For any numbers a, b, and c (c≠0), if a = b, then a/c = b/c What it means: You can divide BOTH sides of an equation by any number, except zero, and the equation will still hold true. Why did we add c ≠ 0?
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2) -6y = 18 Divide both sides by -6. -6y = 18 -6 -6 y = -3 Does -6(-3) = 18? YES! 1) 4x = 24 Divide both sides by 4. 4x = 24 4 4 x = 6 Does 4(6) = 24? YES!
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The one step method: Ex: 2x = 4 3 1. Multiply by the reciprocal. 3 2x = 4 3 2 3 2 x = 6 The two step method: Ex: 2x = 4 3 1. Multiply by 3. (3)2x = 4(3) 3 2x = 12 2. Divide by 2. 2x = 12 2 2 x = 6
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Solve -3v = -129 1. v = -126 2. v = -43 3. v = 43 4. v = 126 Answer Now
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Which step clears the fraction in 1. Multiply by 3 2. Multiply by 5 3. Multiply by -12 4. Multiply by -5 Answer Now
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Solve 1. b = -56 2. b = -14 3. b = 14 4. b = 56 Answer Now
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