8th grade Math Lesson 2-7 Practice problems
1. Solve and determine if the equation has one, none or infinite solutions.
-11 + x = -7x - 8(-x + 1)
2. Solve and determine if the equation has one, none or infinite solutions.
33 + 6x = 3(-1 + 5x)
3. Solve and determine if the equation has one, none or infinite solutions.
-5(x - 1) = 5 - 5x
4. Solve and determine if the equation has one, none or infinite solutions.
12 + 4n = 4(n + 3)
5. Solve and determine if the equation has one, none or infinite solutions.
4(-4 - 8m) + 28m + 4m = -272
1. -11 + x = -7x - 8(-x + 1)
Solve:
-11 + x = -7x + 8x - 8
Combine like terms:
x + 7x - 8x = 8 - 11 + 8
Simplify:
0 = 5
This equation has no solution.
2. 33 + 6x = 3(-1 + 5x)
Simplify:
33 + 6x = -3 + 15x
Combine like terms:
6x - 15x = -3 - 33
Simplify:
-9x = -36
Divide both sides by -9:
x = 4
This equation has one solution.
3. -5(x - 1) = 5 - 5x
Distribute -5:
-5x + 5 = 5 - 5x
Combine like terms:
-5x + 5x = 5 - 5
Simplify:
0 = 0
This equation has infinite solutions.
4. 12 + 4n = 4(n + 3)
Distribute 4:
12 + 4n = 4n + 12
Subtract 4n from both sides:
12 = 12
This equation has infinite solutions.
5. 4(-4 - 8m) + 28m + 4m = -272
Simplify:
-16 - 32m + 28m + 4m = -272
Combine like terms:
-32m + 28m + 4m = -272 + 16
Simplify:
0 = -256
This equation has no solution.
To solve these equations and determine the number of solutions, follow these steps for each equation:
Step 1: Simplify both sides of the equation by distributing and combining like terms if necessary.
Step 2: Move all the variable terms to one side of the equation and all the constant terms to the other side.
Step 3: Combine like terms on each side of the equation.
Step 4: If there are variables on both sides of the equation, move all variables to one side and all constants to the other side.
Step 5: Simplify both sides of the equation further if necessary, combining like terms.
Step 6: Check the resulting equation to determine the number of solutions.
Let's apply these steps to the given practice problems:
1. -11 + x = -7x - 8(-x + 1)
Step 1: -11 + x = -7x + 8x - 8
Step 2: x + 11 = x - 8
Step 3: 11 = -8 (no like terms to combine)
Step 4: 0 = -19 (moved variables to one side)
Step 5: The equation simplifies to 0 = -19
Step 6: Since 0 and -19 are not equal, the equation has no solution.
2. 33 + 6x = 3(-1 + 5x)
Step 1: 33 + 6x = -3 + 15x
Step 2: 6x - 15x = -3 - 33
Step 3: -9x = -36
Step 4: 9x = 36 (multiplied both sides by -1 to isolate x)
Step 5: x = 4 (divided both sides by 9 to solve for x)
Step 6: The equation has one solution.
3. -5(x - 1) = 5 - 5x
Step 1: -5x + 5 = 5 - 5x
Step 2: -5x + 5x = 5 - 5
Step 3: 0 = 0 (no like terms to combine)
Step 4: 0 = 0 (already in this form)
Step 6: Since 0 = 0, the equation has infinite solutions.
4. 12 + 4n = 4(n + 3)
Step 1: 12 + 4n = 4n + 12
Step 2: 4n - 4n = 12 - 12
Step 3: 0 = 0 (no like terms to combine)
Step 4: 0 = 0 (already in this form)
Step 6: Since 0 = 0, the equation has infinite solutions.
5. 4(-4 - 8m) + 28m + 4m = -272
Step 1: -16 - 32m + 28m + 4m = -272
Step 2: -32m + 28m + 4m = -272 + 16
Step 3: 0m = -256
Step 4: 0 = -256 (no variable terms left, only a constant term)
Step 6: Since 0 and -256 are not equal, the equation has no solution.
By following these steps for each equation, you can solve them and determine the number of solutions.
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.