[solving equations][section 9]
(1.) 5n + 3 = 33 here is the problem
-3 -3
subtract 3 from each side
_______________
5n = 30
subtract
____ ___
5 5
divide each side by 5
n = 6 divide and cancel
result: n = 6
(2.) 2n + 3 = 7 here is the problem
-3 -3
subtract 3 from each side
_____________
2n =
4 subtract
___ __
2 2 divide each side by 2
n = 2 divide and cancel
result: n = 2
(3.) 5n - 3 = 17 here is the problem
+
3 + 3 add 3 to each side
_____________
5n = 20
add
___ _____
5 5
divide each side by 5
n = 4 divide and cancel
result: n = 4
(4.) 3t + 17 = 5 here is the problem
-17 -17
subtract 17 from each side
______________
3t
= -12 subtract
___ ___
3 3
divide each side by 3
t = -4 divide and cancel
result: t = -4
(5.) 2a + 15 = 3 here is the problem
-15 -15
subtract 15 from each side
_______________
2a
= -12 subtract
____ ___
2 2 divide each side by 2
a = -6 divide and cancel
result: a = -6
(6.) 3n - 17 = 4 here is the problem
+17 +17 add 17 to each side
_______________
3n =
21 add
___ ___
3 3
divide each side by 3
n = 7 divide and cancel
result:
n = 7
(7.) 9a - 1 = 80 here is the problem
+
1 + 1 add 1 to each side
________________
9a
= 81 add
___ ___
9 9 divide each side by 9
a = 9 divide and cancel
result:
a = 9
(8.) 5 - 3a = 32
-5 + 3a = -32 multiply thru by -1
+
5 + 5 add 5 to each side
________________
3a = -27 add
____ ____
3 3 divide each side by 3
a = -9 divide and cancel
result:
a = -9
(9.) 5 - 2y = 15 here is the problem
-5 + 2y = -15 multiply thru by -1
+
5 + 5 add 5 to each side
_________________
2y = -10 add
_____ ______
2 2
divide each side by 2
y = -5 divide and cancel
result: y = -5
(10.) 7 = 6x + 19 here is the problem
6x + 19 = 7 rearrange like this
-19 -19
subtract 19 from each side
___________________
6x = -12 subtract
_______ ______
6 6 divide each side by 6
x = -2 divide and cancel
result: x = -2
(11.) 8 = 5y + 33
5y + 33 = 8 rearrange like this
-33 -33
subtract 33 from each side
_________________
5y
= -25 subtract
___ ____
5 5 divide each side by 5
y = -5 divide and cancel
result:
y = -5
(12.) -5 = 32 - 3b here is the problem
32 - 3b = -5 rearrange like this
-32 + 3b = 5 multiply thru by -1
+
32 + 32 add 32 to each side
_________________
3b = 37 add
___ ___
3 3
divide each side by 3
b = 12 1/3 change to mixed number, and cancel
result: b = 12 1/3
(13.) 4 = 30 - 6t here is the problem
30 - 6t = 4 rearrange like this
-30 + 6t = -4 multiply thru by -1
+30
+ 30 add 30 to each side
___________________
6t = 26 add
___ ___
6 6 divide each side by 6
t = 13/3 reduce and cancel
t = 4 1/3 write as a mixed number
result: t = 4 1/3
(14.) 15 - (5/4)v = 23 here is the problem
-15 + (5/4)v = -23 multiply thru by -1
+ 15
+ 15 add 15 to each side
________________________
(5/4)v = -8
add
(4/5)(5/4)v = (-8)(4/5) multiply each side by 4/5
v = -32/5 cancel and multiply
v = -6.4 divide
result: v = -6.4
(15.) 6 = 26 + (2/5)n
26 + (2/5)n = 6 rearrange like this
-26 -26 subtract 26 from each side
_____________________
(2/5)n = -20 subtract
(5/2)(2/5)n = (-20)(5/2) multiply each side by 5/2
n = -50 cancel and multiply
result: n = -50
(16.) 0 = (7/10)n - 35 here is the problem
+ 35 + 35 add 35 to each side
_________________________
35 = (7/10)n add
10*35 = 10(7/10)n multiply each side by 10
350 = 7n multiply and cancel
_____ ____
7 7 divide each side by 7
50 = n divide and cancel
result: n = 50
(17.) (2/3)t - 13 = 57 here is the problem
+ 13 +13
add 13 to each side
______________________
(2/3)t = 70 add
(3/2)(2/3)t = (3/2)(70) multiply each side by 3/2
t = 105 multiply and cancel
result: t = 105
(18.) 49 + (3/5)x = 16 here is the problem
-49 -49
subtract 49 from each side
________________________
(3/5)x = -33 subtract
(5/3)(3/5)x = (-33)(5/3) multiply ea side by 5/3
x = -55 multiply and cancel
result: x = -55
(19.) 0 = 0.6n - 3.6 here is the problem
+
3.6 + 3.6
add 3.6 to each side
______________________
3.6 = 0.6n add
____
____
0.6
0.6 divide each
side by 0.6
6 = n divide and cancel
result: n = 6
(20.) (3/4)x - 3 = 18 here is the problem
+3 +3
add 3 to each side
______________________
(3/4)x =
21 add
(4/3)(3/4)x = (4/3)(21) multiply each side by 4/3
x = 28 multiply and cancel
result: x = 28