One-step equations. Vocabulary

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1 Review solvig oe-step equatios with itegers, fractios, ad decimals. Oe-step equatios Vocabulary equatio solve solutio iverse operatio isolate the variable Additio Property of Equality Subtractio Property of Equality A equatio uses a equal sig to show that two expressios are equal. All of these are equatios. + = r + = = x 00 = 50 To solve a equatio, fid the value of the variable that makes the equatio true. This value of the variable is called the solutio of the Additioal Example : Determiig Whether a Number is a Solutio of a Equatio Determie which value of x is a solutio of the x + = 5; x = 5,, or Substitute each value for x i the x + = = 5 = 5 So 5 is ot solutio. Substitute 5 for x. Additioal Example Cotiued Determie which value of x is a solutio of the x + = 5; x = 5,, or Substitute each value for x i the x + = 5 + = 5 5= 5 So is a solutio. Substitute for x.

2 Additioal Example Cotiued Determie which value of x is a solutio of the x + = 5; x = 5,, or Substitute each value for x i the x + = 5 + = 5 = 5 So is ot a solutio. Substitute for x. Try This: Example Determie which value of x is a solutio of the x = ; x = 9,, or Substitute each value for x i the x = 9 = 5 = So 9 is ot a solutio. Substitute 9 for x. Try This: Example Cotiued Determie which value of x is a solutio of the x = ; x = 9,, or Substitute each value for x i the x = = = So is a solutio. Substitute for x. Try This: Example Cotiued Determie which value of x is a solutio of the x = ; x = 9,, or Substitute each value for x i the x = = = So is ot a solutio. Substitute for x. Additio ad subtractio are iverse operatios, which meas they udo each other. To solve a equatio, use iverse operatios to isolate the variable. This meas gettig the variable aloe o oe side of the equal sig. To solve a subtractio equatio, like y 5 =, you would use the Additio Property of Equality. ADDITION PROPERTY OF EQUALITY Words Numbers Algebra You ca add the same umber to both sides of a equatio, ad the statemet will still be true. + = = 9 x + z = y + z

3 There is a similar property for solvig additio equatios, like x + 9 =. It is called the Subtractio Property of Equality. SUBTRACTION PROPERTY OF EQUALITY Words Numbers Algebra You ca subtract the same umber from both sides of a equatio, ad the statemet will still be true. + = + = x z = y z Additioal Example A: Solvig Equatios Usig Additio ad Subtractio Properties A. 0 + = 0 + = = 0 + = = Subtract 0 from both sides. 0 + = = Idetity Property of Zero: 0 + =. Additioal Example B: Solvig Equatios Usig Additio ad Subtractio Properties B. p = 9 p = Add to both sides. p + 0 = p = Idetity Property of Zero: p + 0 = p. p = 9 = 9 9 = 9 Additioal Example C: Solvig Equatios Usig Additio ad Subtractio Properties C. = y = y + + Add to both sides. = y + 0 = y Idetity Property of Zero: y + 0 = 0. = y = = A. 5 + = = = = 9 9 = 9 Try This: Example A Subtract 5 from both sides. 0 + = = Idetity Property of Zero: 0 + =. B. p = p = + + Try This: Example B Add to both sides. p + 0 = p = Idetity Property of Zero: p + 0 = p. p = = =

4 Try This: Example C C. = y = y + + Add to both sides. = y + 0 = y Idetity Property of Zero: y + 0 = 0. = y = = Lear to solve equatios usig multiplicatio ad divisio. Vocabulary Divisio Property of Equality Multiplicatio Property of Equality You ca solve a multiplicatio equatio usig the Divisio Property of Equality. DIVISION PROPERTY OF EQUALITY Words Numbers Algebra You ca divide both sides of a equatio by the same ozero umber, ad the equatio will still be true. = = = z z Additioal Example : Solvig Equatios Usig Divisio Solve x =. Solve 9x =. Try This: Example x = x = x = x = x = () = = Divide both sides by. x = x Substitute for x. 9x = 9x = Divide both sides by x = x = x x = 9x = 9() = Substitute for x. =

5 You ca solve a divisio equatio usig the Multiplicatio Property of Equality. MULTIPLICATION PROPERTY OF EQUALITY Words Numbers Algebra You ca multiply both sides of a equatio by the same umber, ad the statemet will still be true. = = = z x = z y Additioal Example : Solvig Equatios Usig Multiplicatio Solve =. = Multiply both sides by. = 9 = 9 = Substitute 9 for. = Try This: Example Solve = = Multiply both sides by. = Lear to solve equatios with itegers. = Substitute for. = = Whe you are solvig equatios with itegers, your goal is the same as with whole umbers: isolate the variable o oe side of the Recall that the sum of a umber ad its opposite is 0. Whe you add the opposite to get 0, you ca isolate the variable ( ) = 0 a + ( a) = 0 Additioal Example A & B: Addig ad Subtractig to Solve Equatios A. B. x = x = x + = + x = 5 + r = r = r = r = Add to both sides. Commutative Property x + = 0 Add 5 to both sides. 5

6 Additioal Example C & D: Addig ad Subtractig to Solve Equatios Cotiued C. D. + = + = = z + = z + = z = 9 The variable is already isolated. Add itegers. Add to each side. Try This: Example A & B A. p = 9 p = 9 p + = 9 + Add to both sides. p = Commutative Property p + = B. + g = g = g = 5 + Add to both sides. g = C. D. + = r + = r Try This: Example C & D = r a + 9 = 9 a + 9 = a = The variable is already isolated. Add itegers. Add 9 to each side. Additioal Example A: Multiplyig ad Dividig to Solve Equatios Cotiued A. 5x = 5 5x = x = Divide both sides by 5. Additioal Example B: Multiplyig ad Dividig to Solve Equatios Cotiued Try This: Example A B. z = 5 z = 5 Multiply both sides by. A. x = x = Divide both sides by. z = 0 x =

7 Try This: Example B. z = 9 z = 9 Multiply both sides by. z = Oe-Step Equatios with Ratioal Numbers (fractios ad decimals) Additioal Example A: Solvig Equatios with Additioal Examples B: Solvig Equatios with Decimals. Decimals A. m +. = 9 B..p =. m +. = 9. =. m =. Remember! Subtract. from both sides. Oce you have solved ad equatio it is a good idea to check your aswer. To check your aswer, substitute your aswer for the variable i the origial.p. = p =.. Divide both sides by. Additioal Examples C: Solvig Equatios with Decimals x C. = 5.. x =. 5 Multiply both sides by.. x = A. m + 9. = Try This: Example A & B m + 9. = 9. = 9. m =. B. 5.5b = b 5.9 = b =. Subtract 9. from both sides. Divide both sides by 5.5

8 y C. = y = y = 05 Try This: Examples C Multiply both sides by.5 Additioal Examples A: Solvig Equatios with Fractios A. + = + = = 5 Subtract from both sides. Additioal Examples B: Solvig Equatios with Fractios B. y = = + y + Add to both sides. y = + Fid a commo deomiator;. y = 5 Simplify. Additioal Examples C: Solvig Equatios with Fractios 5 C. 5 x 5 = 5 = 5 x 5 x = Multiply both sides by. 5 Simplify. Try This: Example A Try This: Example B A. + 9 = = = Subtract 9 Simplify. 9 from both sides. B. y = = + y + Add to both sides. y = + y = Fid a commo deomiator;. Simplify.

9 C. x = 9 x = 9 Try This: Examples C = x 9 x = 9 Multiply both sides by. Simplify. 9

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