Variables on Both Sides
8x - 3 = 5x + 18
x = 7
6/x = 3/5
x = 10
x = 10, -2
A = lw
Solve for l
l = a/w
The larger number is 10 more than twice the smaller number. Their sum is 64. Find both numbers.
18 and 46
3(2x + 5) = 4x + 27
x = 3
(x + 2)/4 = (x - 1)/3
x = 10
|3x + 2| = 11
x = 3, -13/3
P = 2l + 2w Solve for w
w = (p - 2l)/2
Find three consecutive even integers such that twice the smallest plus three times the largest equals 74.
14, 16, and 18
5 - 2(x - 4) = 3x - 10
x = 3
(x - 5)/2 = (x + 1)/4
x = 11
2|x + 5| = 14
x = 2, -12
y = 4x + 9 Solve for x
x = (y - 9)/4
The length of a rectangle is 4 less than three times its width. The perimeter is 72 cm. Find its dimensions.
10 and 26
4(3x - 2) - 5x = 2(x + 7)
x = 22/5
5/(x + 1) = 1/2
x = 9
|5x - 4| = 16
x= 4, -12/5
F = (9/5)C + 32 Solve for C
C = (5/9)(F - 32)
A restaurant sells 120 fewer hotdogs than hamburgers. Altogether, it sells 560 hotdogs and hamburgers. How many of each does it sell?
340 hamburgers; 220 hotdogs
6(x - 2) + 3 = 2(3x - 5)
Infinitely Many Solutions
(2x + 1)/3 = (x - 4)/2
x = -14
-3|x -2| + 6 = -9
x = 7, -3
v = tr^2h solve for h
h = v/tr^2
The larger of two numbers is 7 more than twice the smaller. The sum of twice the smaller number and three times the larger number is 101. Find both numbers.
17 and 41