1. Solve and determine if the equation has one, none or infinite solutions.
-11 + x = -7x - 8(-x + 1)
To solve this equation, we will simplify the expressions on both sides:
-11 + x = -7x - 8(-x + 1)
-11 + x = -7x + 8x - 8
Next, we will combine like terms on both sides:
-11 + x = -7x + 8x - 8
x - 7x - 8x = -11 + 8
-14x = -3
Dividing both sides by -14:
x = -3 / -14
x = 3/14
The equation has one solution.
2. Solve and determine if the equation has one, none or infinite solutions.
33 + 6x = 3(-1 + 5x)
To solve this equation, we will distribute the 3 on the right side:
33 + 6x = 3(-1) + 3(5x)
33 + 6x = -3 + 15x
Next, we will combine like terms on both sides:
33 + 6x = -3 + 15x
6x - 15x = -3 - 33
-9x = -36
Dividing both sides by -9:
x = -36 / -9
x = 4
The equation has one solution.
3. Solve and determine if the equation has one, none or infinite solutions.
-5(x - 1) = 5 - 5x
To solve this equation, we will distribute the -5 on the left side:
-5x + 5 = 5 - 5x
Next, we will combine like terms on both sides:
-5x + 5 = 5 - 5x
-5x + 5x = 5 - 5
0 = 0
The equation has infinite solutions since both sides are equal regardless of the value of x.
4. Solve and determine if the equation has one, none or infinite solutions.
12 + 4n = 4(n + 3)
To solve this equation, we will distribute the 4 on the right side:
12 + 4n = 4n + 12
Next, we will combine like terms on both sides:
12 + 4n = 4n + 12
4n - 4n = 12 - 12
0 = 0
The equation has infinite solutions since both sides are equal regardless of the value of n.
5. Solve and determine if the equation has one, none or infinite solutions.
4(-4 - 8m) + 28m + 4m = -272
To solve this equation, we will simplify the expressions on both sides:
4(-4 - 8m) + 28m + 4m = -272
-16 - 32m + 28m + 4m = -272
Next, we will combine like terms on both sides:
-16 - 32m + 28m + 4m = -272
-16 - 32m + 32m = -272
-16 = -272
Since -16 is not equal to -272, the equation has no solutions.