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Writing and Solving Equations

Writing and Solving Equations. 3.5 Equations with the Variable on both sides. Solve. 1/3(12 – 6x) = 4 – 2x 12-6x = 12-6x 12=12 How often does 12 = 12? The solution is all real numbers. 5u + 5(1 – u) = u + 8 5u + 5 -5u = u +8 5 = u + 8 -3 = u. Solve. 3(m + 5) -6 = 3(m + 3)

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Writing and Solving Equations

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  1. Writing and Solving Equations 3.5 Equations with the Variable on both sides.

  2. Solve 1/3(12 – 6x) = 4 – 2x 12-6x = 12-6x 12=12 How often does 12 = 12? The solution is all real numbers. 5u + 5(1 – u) = u + 8 5u + 5 -5u = u +8 5 = u + 8 -3 = u

  3. Solve. 3(m + 5) -6 = 3(m + 3) 3m +15 = 3m +9 15 = 9 How often does 15 = 9? The answer is no solution. 6r – 2(2 – r) = 4(2r – 1) 6r -4 +2r = 8r -4 8r -4 = 8r – 4 All real numbers.

  4. Write an equation and solve. • Find a number whose product with nine is the same as its sum with 56. 9 x = x +56 8x = 56 x = 7

  5. Write an equation and solve. • Three times a number, decreased by 8, is the same as twice the number, increased by 15. Find the number. 3x-8 = 2x+15 x = 23

  6. Write an equation and solve. • The sum of two numbers is 15. Three times one of the numbers is 11 less than five times the other. Find the numbers. x + y = 15 3x = 5y-11 Solve

  7. Write an equation and solve. • The lengths of the sides of a triangle are consecutive even integers. Find the length of the longest side if it is 22 cm shorter than the perimeter. x + (x+1) + (x+2) = P (x+2) = P -22 or (x+2) +22 = P Now solve.

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