[solving equations part 3][section 15]
(1.) 5x = 2x + 12 here is the problem
-2x
-2x subtract 2x from each
side
___________________
3x = 12
subtract
___ ___
3 3 divide each side by 3
x = 4 divide and cancel
result: x = 4
(2.) 7y + 8 = 11y here is the problem
11y = 7y + 8 rearrange like this
-7y
-7y subtract 7y from each
side
_________________
4y = 8
subtract
_____ _______
4 4 divide each side by 4
y = 2 divide and cancel
result: y = 2
(3.) -7m = 9m - 12 here is the problem
7m = -9m + 12 multiply thru by -1
+
9m +9m add 9m to each side
_____________________
16m = 12 add
____ ___
16 16 divide each side by 16
m = 3/4 reduce and cancel
result: m = 3/4
(4.) 4a - 5 = 7a - 7 here is the problem
-4a + 5 = -7a + 7 multiply thru by -1
+7a + 7a add 7a to each side
_______________________
3a + 5 = 7
add
-5 -5 subtract 5 from each side
_______________________
3a =
2 subtract
___ ______
3 3 divide each side by 3
a = 2/3 cancel
result: a = 2/3
(5.) -6x - 7 = -5x + 3 here is the problem
6x + 7 = 5x - 3 multiply thru by -1
-5x -5x subtract 5x from each side
_________________________
x + 7 = -3 subtract
-7 -7 subtract 7 from each side
____________________
x =
-10 subtract
result: x = -10
(6.) -3r - 8 = -5r + 12 here is the problem
+
5r + 5r add 5r to each side
_________________________
2r - 8 = 12
add
+ 8 +
8 add 8 to each side
________________________
2r = 20 add
___ ___
2
2 divide each side by 2
r = 10 divide and cancel
result: r = 10
(7.) q + 7q = -12q + 10 here is the problem
8q = -12q + 10 combine like terms
+ 12q +12q
add 12q to each side
_____________________
20q = 10 add
_____ _____
20 20 divide each side by 20
q = 1/2 reduce and cancel
result: q = 1/2
(8.) 4(x + 2) = 3x here is the problem
4x + 8 = 3x multiply thru parentheses
-8
-8 subtract 8 from each
side
__________________
4x = 3x - 8 subtract
-3x -3x
subtract 3x from each side
_____________________
x =
-8 subtract
result: x = -8
(9.) 5(m - 5) = 3(m + 1) here is the problem
5m - 25 = 3m + 3 multiply thru parentheses
+ 25
+ 25 add 25 to each side
________________________
5m = 3m + 28 add
-3m -3m subtract 3m from each side
__________________________
2m =
28 subtract
___ ___
2 2 divide each side by 2
m = 14 divide and cancel
result: m = 14
(10.) 7y = -2(y + 9) here is the problem
7y = -2y - 18 multiply thru parentheses
+2y +2y add 2y to each side
_____________________
9y = -18 add
____ _____
9 9 divide each side by 9
y = -2 divide and cancel
result: y = -2
(11.) -4(a - 5) = -7(a - 2) + 6 here is the problem
-4a + 20 = -7a + 14 + 6 multiply thru parentheses
-4a + 20 = -7a + 20 combine like terms
+7a + 7a add 7a to each side
________________________
3a + 20 = 20
add
-20 -20
subtract 20 from each side
___________________________
3a = 0 subtract
____ ____
3 3 divide each side by 3
a = 0 divide and cancel
result: a = 0
(12.) 36 - 2(c - 28) = -4(2c + 52) here is the problem
36 - 2c + 56 = -8c - 208 multiply thru
-2c + 92 = -8c - 208 combine
like terms
+ 8c + 8c add 8c to each side
__________________________
6c + 92 = -208 add
-92 -92 subtract 92 fr ea side
________________________
6c =
-300 subtract
____ ____
6 6 divide each side by 6
c = -50 divide and cancel
result: c = -50