Answer:
1.) x = 5
2.) n = 0
3.) m = 5
4.) r = -8 or r = 8
5.) x = 10 or x = -53/5
Explanation:
1.) -37 + 4x = -7x -6(x - 8)
-37 + 4x = -7x - 6x + 48 Multiply -6(x - 8)
-37 + 4x = -13x + 48 Combine like terms
4x = -13x + 85 Add 37 to both sides
17x = 85 Add 13x to both sides
x = 5 Divide both sides by 17
2.) 3(2n + 7) = -7(-3 + 5n) - 7n
6n + 21 = 21 -35n - 7n Multiply 3(2n + 7) and -7(-3 + 5n)
6n + 21 = 21 - 42n Combine like terms
6n = -42n Subtract 21 from both sides
48n = 0 Add 42n to both sides
n = 0 Divide both sides by 48
3.) 1 - 8m = -9 - 6m
-8m = -6m - 10 Subtract 1 from both sides
-2m = -10 Add 6m to both sides
m = 5 Divide both sides by -2
4.) |r/8| = 1
If the lines mean absolute value, 8/8 equals 1; When you take the absolute value of -8/8, it becomes 8/8 with equates to 1.
5.) | 10x + 3| = 103
|10x| = 100 Subtract 3 from both sides
x = 10 Divide both sides by 10
OR
Apply absolute rule: If |u | = a; a > 0 then u = a or u = -a
10x + 3 = -103
10x = -106 Subtract 3 from both sides
x = -10.6 Divide both sides by 10
(-10.6 is -53/5 as a fraction)
To check:
-53 ÷ 5 = -10.6, multiply that by 10 to get -106. Add 3; -103. Then take the absolute value of that: 103.
Hope this helps,
♥A.W.E.S.W.A.N.♥
