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Solving Equations

Solving Equations . Ashley Painter . How do you solve an equation?. An equation says that two expressions are equal to each other. The goal of solving an equation is to get the variable (x, n, y, etc.) by itself.

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Solving Equations

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  1. Solving Equations Ashley Painter

  2. How do you solve an equation? • An equation says that two expressions are equal to each other. • The goal of solving an equation is to get the variable (x, n, y, etc.) by itself. • To get the variable by itself, you must get rid of all the other numbers in the equation. • Go to http://www.mathsisfun.com/algebra/equations-solving.htmlor http://www.regentsprep.org/regents/math/algebra/ae2/lsolveq.htm for a crash-coarse on solving equations.

  3. How do you get x alone? • To get rid of all the other numbers, you must do the inverse operations. • An inverse operation is an operation that reverses the effect of another operation. • The inverse operations are: • Addition Property of Equality- reverses a subtraction problem • Subtraction Property of Equality- reverses an addition problem • Multiplication Property of Equality- reverses a division problem • Division Property of Equality- reverses a multiplication problem

  4. Solving an Equation: Addition Property of Equality (One Step Equations) To “keep it equal” on both sides, whatever you do to one side you MUST do to the other. We used the addition property of equality to get the variable by itself. On example number 1, originally it said to add 5 to X. To reverse this we subtracted 5 from each side. The 5 canceled out and when we take the 5 away from 7, we get 2. Try numbers 2 and 3 by yourself. 1. X+5= 7 -5 -5 X = 2 2. 20+X= 22 -20 -20 X = 2 3. N+7= 10 -7 -7 N= 3

  5. Solving an Equation: Subtraction Property of Equality (One Step Equations) To “keep it equal” on both sides, whatever you do to one side you MUST do to the other. 1. X-5= 7 +5 +5 X = 12 2. X-30= 20 +30 +30 X = 50 3. N-7= 10 +7 +7 N= 17 We used the subtraction property of equality to get the variable by itself. On example number 1, originally it said to subtract 5 from X. To reverse this we add 5 to each side. The 5 canceled out and when we add the 5 and 7, we get 2. Try numbers 2 and 3 by yourself.

  6. Solving an Equation: Multiplication Property of Equality (One Step Equations) To “keep it equal” on both sides, whatever you do to one side you MUST do to the other. 1. Yx5= 25 55 Y= 5 2. X6= 30 6 6 X = 5 3. Nx2= 10 22 N= 5 We used the multiplication property of equality to get the variable by itself. On example number 1, originally it said to multiply Y and 5. To reverse this we divide each side by 5. The 5 canceled out and when we divide 25 by 5, we get 5. Try numbers 2 and 3 by yourself.

  7. Solving an Equation: Division Property of Equality (One Step Equations) To “keep it equal” on both sides, whatever you do to one side you MUST do to the other. 1. Y4=10 44 Y= 40 2. X6= 5 6 6 X = 30 3. N/20= 2 x20x20 N= 40 We used the division property of equality to get the variable by itself. On example number 1, originally it said to divide Y by 4. To reverse this we multiply each side by 4. The 4 canceled out and when we multiply 10 by 4, we get 40. Try numbers 2 and 3 by yourself.

  8. Solving an Equation: Using the Addition, Subtraction, Multiplication, and Division Property of Equality (Two Step Equations) Remember to combine like-terms. 3. X5 -5= 20 +5 +5 X5= 25 5 5 X= 5 4. X8 -5 = 0 +5 +5 X8= 5 8 8 X= 40 5. N-2 = 2 2 2 2 N-2= 4 +2 +2 N= 6 6. 20+X +2 = 4 11 -2 -2 20+X =2 11 11 11 20 +X= 22 -20 -20 X=2 1. X+5 -2= 5 +2 +2 X+5=7 -5 -5 X= 2 2. 20+X+2= 24 (combine 20 and 2) 22+X= 24 -22 -22 X=2

  9. Distributing in Multistep Equations • 2(x+5) =14 2x+10= 14 -10 -10 2x= 4 2 2 x= 2 • Distribution- opposite of factoring; multiplying out parts of an expression; the number on the outside of the parenthesis multiplies all terms inside the parenthesis • When there are parenthesis, multiply the numbers inside them by the number outside them. In the example, the 2 is the outside number. We multiplied the 2 by x (giving us 2x) and by 5 (giving us 10).

  10. Solving Multistep Equations 1. 133=7(1+3a) 133=7+21a -7 -7 126=21a 21 21 6=a 2. 4p+14=6(p-3)+2p 4p+14=6p-18+2p (combine 6p and 2p) 4p+14=8p-18 -4p -4p 14=4p-18 +18 +18 32=4p 4 4 8=p 3. N-2 = 2 2 2 2 N-2= 4 +2 +2 N= 6 Multistep equations have 3 or more steps. Start with subtraction or addition and then move to multiplication or division. However if there was an equation like the example below, you would start by multiplying each side by 2 as shown.

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