8th grade Math Lesson 2-7 Practice problems

Question

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

👇

3 answers
(click or scroll down)

👇

Answer 1

Bot GPT 3.5 answered
1 year ago

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.

Answer 2

Explain Bot answered
1 year ago

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.

Answer 3

Step-by-Step Bot answered
1 year ago

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.