Three times a number minus 35 is 79. 9n – (6/n) n or 4n (11 + n) or 3(n + 11) 4n2 + 5n n or 7n + 23 Three times a number.

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Three times a number minus 35 is 79. 9n – (6/n) 100 + 4n or 4n + 100 3(11 + n) or 3(n + 11) 4n2 + 5n 23 + 7n or 7n + 23 Three times a number minus 35 is 79. Two times the sum of a number cubed and three times the same number squared equals 4 times that same number. The quotient of 5 times a number and the sum of 3 and that number equals that number minus eight.

Solve the Equation. Check your solution. 17 = 9 – a #2 17 = 9 – a Original problem. 9 – a = 17 Rewrite the problem. -9 -9 Move 9 to other side. -1a = 8 Simplify. -1 -1 Move -1 to other side. a = -8 Final Answer. Check a = -8 Substitute -8 into original problem. 17 = 9 – a 17 = 9 – (-8) 17 = 9 + 8 yes.

Solve the Equation. Check your solution. (2/3)m = ½ #4 (2/3)m = ½ Original problem. (2/3)m = ½ Rewrite the problem. (2/3) (2/3) Move 2/3 to other side. m = 3/1 Simplify. m = 3 Final Answer. Check m = 3 Substitute 3 into original problem. (2/3)m = ½ (2/3)(3/1) = ½ yes.

Solve the Equation. Check your solution. -8 = -2(z + 7) #6 -8 = -2(z + 7) Original problem. -2(1z + 7) = -8 Rewrite the problem. -2(1z + 7) = -8 Do the Distributive Property. -2z – 14 = -8 Simplify. +14 +14 Move -14 to other side. -2z = 6 Simplify. -2 -2 Move -2 to other side. z = -3 Simplify. z = -3 Final Answer. Check z = -3 Substitute -3 into original problem. -8 = -2(z + 7) -8 = -2(-3 + 7) -8 = -2(4) yes.

Solve the Equation. Check your solution. 3x + 17 = 5x – 13 #8 3x + 17 = 5x – 13 Original problem. 5x – 13 = 3x + 17 Rewrite the problem. -3x -3x Move 3x to other side. 2x – 13 = 17 Simplify. +13 +13 Move -13 to other side. 2x = 30 Simplify. 2 2 Move 2 to other side. x = 15 Simplify. x = 15 Final Answer. Check x = 15 Substitute 15 into original problem. 3x + 17 = 5x – 13 3(15) + 17 = 5(15) – 13 45 + 17 = 75 – 13 62 = 62 yes.

Solve the Equation. Check your solution. 120 – (3/4)y = 60 #10 120 – (3/4)y = 60 Original problem. 120 – (3/4)y = 60 Rewrite the problem. -120 -120 Move 120 to other side. (-3/4)y = -60 Simplify. (-3/4) (-3/4) Move -3/4 to other side. y = 80 Simplify. y = 80 Final Answer. Check y = 80 Substitute 80 into original problem. 120 – (3/4)y = 60 120 – (3/4)(80) = 60 120 – 60 = 60 60 = 60 yes.

Solve the Equation. Check your solution. 4.5 + 2p = 8.7 #12 4.5 + 2p = 8.7 Original problem. 2p + 4.5 = 8.7 Rewrite the problem. -4.5 -4.5 Move 4.5 to other side. 2p = 4.2 Simplify. 2 2 Move 2 to other side. p = 2.1 Simplify. p = 2.1 Final Answer. Check p = 2.1 Substitute 2.1 into original problem. 4.5 + 2p = 8.7 4.5 + 2(2.1) = 8.7 4.5 + 4.2 = 8.7 8.7 = 8.7 yes.

Solve the Equation. Check your solution. 100 = 20 – 5p #14 100 = 20 – 5p Original problem. 20 – 5p = 100 Rewrite the problem. -20 -20 Move 20 to other side. -5p = 80 Simplify. -5 -5 Move -5 to other side. p = -16 Simplify. p = -16 Final Answer. Check p = -16 Substitute -16 into original problem. 100 = 20 – 5p 100 = 20 – 5(-16) 100 = 20 – (-80) 100 = 100 yes.

Solve each formula for the specified variable. a = 3b – c ; for b. Original problem. a = 3b – c Rewrite formula. + c + c Move c to other side to isolate 3b. a + c = 3b Simplify. 3b = a + c Rewrite the problem to work left to right. 3 3 Move 3 to other side to isolate b. b = (a + c)/3 Simplify. b = (a + c)/3 or (1/3)(a + c) Final Answer.

Solve each formula for the specified variable. h = 12g – 1 ; for g. Original problem. h = 12g – 1 Rewrite formula. + 1 + 1 Move 1 to other side to isolate 12g. h + 1 = 12g Simplify. 12g = h + 1 Rewrite the problem to work left to right. 12 12 Move 12 to other side to isolate g. g = (h + 1)/12 Simplify. b = (h + 1)/12 or (1/12)(h + 1) Final Answer.

Solve each formula for the specified variable. 2xy = x + 7 ; for x. Original problem. 2xy = x + 7 Rewrite formula. - x - x Move x to other side to get x’s all on one side. 2xy – x = 7 Simplify. x(2y – 1) = 7 Use Distributive Property to factor out an x. (2y – 1) (2y – 1) Move (2y – 1) to other side to isolate x. (2y – 1) is treated as a single number. x = 7/(2y – 1) Simplify. x = 7/(2y – 1) Final Answer.

Solve each formula for the specified variable. 3(2j – k) = 108 ; for j. Original problem. 3(2j – k) = 108 Rewrite formula. 3 3 Move 3 to other side to get (2j – k) isolated. 2j – 1k = 36 Simplify. + 1k + 1k Move 1k to other side to isolate 2j. 2j = 1k + 36 Simplify. 2 2 Move 2 to other side to isolate j. j = (k + 36)/2 Simplify. j = (k + 36)/2 or (1/2)(k + 36) Final Answer.

Solve each formula for the specified variable. m/n + 5m = 20 ; for m. Original problem. m/n + 5m = 20 Rewrite formula. n[(m/n + 5m = 20] Multiply equation by n to get rid of fractions. m + 5mn = 20n Simplify. m(1 + 5n) = 20n Use Distributive Property to factor out an m. m(5n + 1) = 20n Rewrite formula. (5n + 1) (5n + 1) Move (5n + 1) to other side to isolate m. m = 20n/(5n + 1) Simplify. m = 20n/(5n + 1) Final Answer.