Answers and Explanations 139
Answers
1–100
36.
x = 15
4
Put all terms involving x on one side of the equation and all constants on the other
side, combining all like terms. Finally, divide by the coefficient of x (that is, multiply
both sides by the reciprocal of the coefficient) to get the solution:
5
3
5 1
3
10
5
3
1
3
10 5
4
3
5
3
4
5
15
4
x
x
x
x
x
x
x
+ =
+
−
= −
=
= ( )
=
37.
x =
−
−
10 3 2
2
5
Distribute to remove the parentheses. Then put all terms involving x on one side of the
equation and all constants on the other side, combining all like terms. Finally, divide
by the coefficient of x to get the solution:
2
3
5
2 0
2
3 2
5
100
2
5
10 3 2
2
5
10 3 2
10 3 2
2
(
)
x
x
x
x
x
x
x
x
+ =
+
(
)
+
=
+
−
= −
−
(
) = −
= −
− 5 5
38.
x = –3, 7
This quadratic factors without too much trouble using trial and error:
x
x
x
x
2
4
21 0
7
3 0
−
− =
−
+ =
(
)(
)
Setting each factor equal to zero gives you x – 7 = 0 so that x = 7 is a solution and
x + 3 = 0 so that x = –3 is a solution.