3-4 Solving Equations with Variables on Both Sides - Math Slide Show

Lesson 3-4Objective - To solve equations <strong>with</strong> thevariable on both sides.3x + 7 = 5x −193x + 7 = 5x −193x + 7 = 5x −19−3x−3x−5x−5x7 = 2x −19+ 19 + 19− 2x + 7 =−19−7 −726 = 2x− 2x = −262 2−2 −213 = xx = 13First Priority - Isolate the variable on one side.Solve.1) 7x + 5 = 3x −272) x − 1 = 6x + 29−3x− 3x−x− x4x + 5 =−27− 1= 5x + 29−5 − 5−29 −294x = −32− 30 = 5x4 45 5x = −8− 6 = xSolve.3) 5(4 − x) = 3(x −4)4) 2(3x − 1) = 4(10 −2x)20 − 5x = 3x − 12 6x − 2 = 40 − 8x+ 5x + 5x + 8x + 8x20 = 8x −1214x − 2 = 40+ 12 + 12 + 2 + 232 = 8x8 84 = x14x = 4214 14x = 3Jesse began solving the equation below. Find hermistakes and demonstrate a more efficient technique.Jesse’s workBetter Way3(x − 2) = 5x + 18 3(x − 2) = 5x + 183x − 6 = 5x + 18 3x − 6 = 5x + 18+ 6 + 6 −3x−3x3x = 5x + 24 − 6 = 2x + 18−3x − 3x−18 −182x = 24− 24 = 2x2 2x = 122 2− 12 = x0 = 2x + 24− 24 = 2xCollect the variables− 12 = xon one side first!Translate and solve.Ten less than three times a number is the sameas twice the difference of the number and 7.Let x = the number3x − 10 = 2(x −7)3x − 10 = 2x −14−2x−2xx − 10 = −14+ 10 + 10x =−4Translate and solve.Five more than twice a number is 11 less thanthe product of 10 and the number.Let y = the number2y + 5 = 10y −11−2y −2y5 = 8y−11+ 11 + 1116 = 8y8 82 = yPre-Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2011

Lesson 3-4 (cont.)Find the area of the square below.3(x + 2) = 3(3 + 2) = 152x + 92(3) + 9 = 153(x + 2) = 2x +92Area=s3x + 6 = 2x + 92Area = 15−2x−2xx + 6 = 9Area = 225 un−6 −6x = 32Find the value of x if the perimeter of the rectangleis equal to the perimeter of the equilateral triangle.2x + 63x - 4xP = 2l+2wP = 3sP = 2(2x + 6) + 2xP =3(3x −4)2(2x + 6) + 2x = 3(3x −4)4x + 12 + 2x = 9x − 126x + 12 = 9x −12−6x+ 12 − 6x+1224 = 3x8 = xSolve each equation below.a) 3x - 5 = 2x + 12 b) 3x + 8 = 2(x + 4) + x-2x -2x3x + 8 = 2x + 8 + xx - 5 = 123x + 8 = 3x + 8+5 +5-3x -3xx = 178 = 8 True !One SolutionIdentityx = any real numberc) 3x + 2 = 2(x - 1) + x3x + 2 = 2x - 2 + x3x + 2 = 3x - 2-3x -3x2 = -2 False !No SolutionSolve.4) 4(y - 2) + 6y = 7(y - 8) - 3(10 - y)4y - 8 + 6y = 7y - 56 - 30 + 3y10y - 8 = 10y - 86-10y -10y-88 = -86False StatementNo SolutionSolve.5) 3(4 + k) - 2(3k + 4) = 5(k - 3) - (8k - 19)12 + 3k - 6k - 8 = 5k - 15 - 8k + 19-3k + 4 = -3k + 4+3k +3k4 = 4True StatementInfinitely Many Solutionsx = any real numberSolve.2x −1=2x −35 2 3 530( 2 1 ) ( 2 3 )x − = x − 305 2 3 512x − 15= 20x −18−12x−12x− 15 = 8x −18+ 18 + 183=8x8 8x =38Pre-Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2011

Lesson 3-4 (cont.)Marty has $45 and is saving $2 a week. Wayne has$12 and is saving $5 a week. Write linear equationsto find when they will have the same amount.Let x = # of weeks Let y = savingsMartyWayney = 45 + 2xy = 12 + 5x45 + 2x = 12 + 5x−2x−2x45 = 12 + 3x−12 −1233 = 3x3 311 = x 11 weeksWarren High has 3000 students and is growing at250 students per year. Downey High has 5500but is decreasing at 100 students per year. Writeequations to find when the populations will be equal.Let x = # of years Let y = populationWarrenDowneyy = 3000 + 250xy = 5500 - 100x3000 + 250x = 5500 −100x+ 100x + 100x3000 + 350x = 5500−3000 − 3000350x = 2500350 350x ≈ 7.1 ≈ 7.1 yearsPre-Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2011