How Many Solutions?
5x + 2 = 2x + 14
One Solution
The product of a number and 6 is 3 more than 5 times the number.
6x = 3 + 5x
2x + 4 = 14
x=5
8x + 13x = 42
2
8x - 2 = -9 + 7x
-7
10x + 12 = 2(5x + 6)
Infinitely Many Solutions
The quotient of 5 times a number and 7 is equal to 10.
28 + 8x
10(1 + 3x) = -20
-1
p - 1 = 5p + 3p - 8
1
4x + 10 + x = 2.5(2x - 4)
No Solution
Two more than a certain number is 15 less than the product of 7/8 and the number.
x + 2 = 7/8x - 15
4(-x + 4) = 12
1
3n - 5 = -8(6 + 5n)
-1
-1/2(24 + 6x) = -3(x - 4)
No Solution
Two more than 16 times a number is the same as 21 less than the product of -7 and the number.
16x + 2 = -7x - 21
x/2 - 10 = -6
8
-6(1 - 5x) = 54
2
2(4x - 3) - 8 = 4 + 2x
3
1.5(2x - 4) - 1.5x + 3
One Solution
Decreasing -5 times a number by 18 is equal to decreasing 9 times the number by 25.
-5x - 18 = 9x - 25
9x - 7 = -7
0
8= 8x - 4(x + 8)
10
-5(1 - 5x) + 5(-8x - 2) = -4x - 8x
-5