3. Three times a number minus 35 is 79.
9n – (6/n)
n 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.

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

7. 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 = Final Answer.
Check m = 3 Substitute 3 into original problem.
(2/3)m = ½ (2/3)(3/1) = ½ yes.

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

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

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

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

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

13. 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.
Move 3 to other side to isolate b.
b = (a + c)/3 Simplify.
b = (a + c)/3 or (1/3)(a + c) Final Answer.

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

15. Solve each formula for the specified variable.
2xy = x + 7 ; for x. Original problem.
2xy = x Rewrite formula.
- x x Move x to other side to get x’s all on one side.
2xy – x = Simplify.
x(2y – 1) = 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.

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

17. Solve each formula for the specified variable.
m/n + 5m = 20 ; for m. Original problem.
m/n + 5m = 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) = n 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.