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How many solutions are there to the equation below?

220 = 2x - 12x
Group of answer choices

infinitely many

1

2

Flag question: Question 2
Question 21 pts
Solve the equation for x.

17x - 8x - 11 = 100 - 30

Group of answer choices

x = 9

x = -9

x = 23/3

x = 5

Flag question: Question 3
Question 31 pts
How many solutions are there to the equation below?

11x - 99 = 11(x - 9)
Group of answer choices

1

0

infinitely many

Flag question: Question 4
Question 41 pts
Jimmy and Jill are both solving the same equation but have different answers. Who is incorrect, and why?



Jimmy Jill
9(x - 8) + 3 = -15

9x - 8 + 3 = -15

9x - 5 = -15

9x = -10

x =

9(x - 8) + 3 = -15

9x - 72 + 3 = -15

9x - 69 = -15

9x = 54

x = 6

Group of answer choices

Jimmy is incorrect because he used the distributive property incorrectly.

Jimmy is incorrect because he got a fraction as an answer.

Jill is incorrect because she used the distributive property incorrectly.

Jill is incorrect because she combined like terms incorrectly.

Flag question: Question 5
Question 51 pts
Jorge is solving an equation, but he can't remember the next step. Choose the correct next step and the correct final answer.

x + 3(3 + x) = 21 + 2x

x + 9 + 3x = 21 + 2x

?

Group of answer choices

Subtract 9 from both sides; No solutions

Move "x" to one side; x = 12

Use the distributive property; x = 6

Combined like terms; x = 6

13 answers

Let's solve each question one by one.

Question 1:

How many solutions are there to the equation:
\[ 220 = 2x - 12x \]

First, simplify the right side: \[ 220 = 2x - 12x \]
\[ 220 = -10x \]

Now, solve for \( x \): \[ x = \frac{220}{-10} = -22 \]

Since we obtained a single value for \( x \), there is 1 solution.

Question 2:

Solve the equation for \( x \):
\[ 17x - 8x - 11 = 100 - 30 \]

First, simplify both sides: \[ 17x - 8x - 11 = 70 \]
\[ 9x - 11 = 70 \]

Now, add 11 to both sides: \[ 9x = 70 + 11 \]
\[ 9x = 81 \]

Now, divide both sides by 9: \[ x = \frac{81}{9} = 9 \]

So, the answer is x = 9.

Question 3:

How many solutions are there to the equation:
\[ 11x - 99 = 11(x - 9) \]

First, simplify the right side: \[ 11x - 99 = 11x - 99 \]

Both sides are equal, which means the equation is an identity. Therefore, there are infinitely many solutions.

Question 4:

Who is incorrect, and why?

Jimmy's steps:

  1. \( 9(x - 8) + 3 = -15 \)
  2. \( 9x - 8 + 3 = -15 \) (Distributive property is incorrect)
  3. \( 9x - 5 = -15 \)
  4. \( 9x = -10 \)

Jill's steps:

  1. \( 9(x - 8) + 3 = -15 \)
  2. \( 9x - 72 + 3 = -15 \) (Distributive property is correct)
  3. \( 9x - 69 = -15 \)
  4. \( 9x = 54 \)

Since Jimmy made an incorrect application of the distributive property and Jill was correct, then Jimmy is incorrect because he used the distributive property incorrectly.

Question 5:

Choose the correct next step and the correct final answer for:
\[ x + 3(3 + x) = 21 + 2x \]

Starting from: \[ x + 3(3 + x) = 21 + 2x \]

Distribute on the left side: \[ x + 9 + 3x = 21 + 2x \]
Combine like terms: \[ 4x + 9 = 21 + 2x \]

Move \( 2x \) to the left side: \[ 4x - 2x + 9 = 21 \]
\[ 2x + 9 = 21 \]
\[ 2x = 21 - 9 \]
\[ 2x = 12 \]

Now divide by 2: \[ x = 6 \]

So, the correct next step is Use the distributive property; x = 6.

Summary of Answers:

  1. 1
  2. x = 9
  3. Infinitely many
  4. Jimmy is incorrect because he used the distributive property incorrectly.
  5. Use the distributive property; x = 6
How many solutions are there to the equation below?

220 = 2x - 12x
Group of answer choices

infinitely many

1

2

To determine how many solutions there are for the equation

\[ 220 = 2x - 12x, \]

first, simplify the right side:

  1. Combine like terms: \[ 2x - 12x = -10x. \] So the equation can be rewritten as: \[ 220 = -10x. \]

  2. Now, solve for \( x \) by dividing both sides by \(-10\): \[ x = \frac{220}{-10} = -22. \]

Since we arrived at a single value for \( x \), the equation has 1 solution.

So, the answer is 1.

Solve the equation for x.

17x - 8x - 11 = 100 - 30

Group of answer choices

x = 9

x = -9

x = 23/3

x = 5

Let's solve the equation step by step:

Given the equation:

\[ 17x - 8x - 11 = 100 - 30. \]

  1. Simplify both sides:

The left side: \[ 17x - 8x - 11 = 9x - 11. \]

The right side: \[ 100 - 30 = 70. \]

So the equation becomes:

\[ 9x - 11 = 70. \]

  1. Now, we want to isolate \( x \). First, add 11 to both sides:

\[ 9x - 11 + 11 = 70 + 11 \]

This simplifies to:

\[ 9x = 81. \]

  1. Finally, divide both sides by 9:

\[ x = \frac{81}{9} = 9. \]

So the solution is:

x = 9.

How many solutions are there to the equation below?

11x - 99 = 11(x - 9)
Group of answer choices

1

0

infinitely many

To determine how many solutions there are for the equation

\[ 11x - 99 = 11(x - 9), \]

we can simplify both sides.

  1. Start with the right side: \[ 11(x - 9) = 11x - 99. \]

  2. Now the equation becomes: \[ 11x - 99 = 11x - 99. \]

  3. Notice that both sides are identical. This means that the equation holds true for all values of \( x \).

Since both sides are equal regardless of the value of \( x \), there are infinitely many solutions to the equation.

So the answer is infinitely many.

Jimmy and Jill are both solving the same equation but have different answers. Who is incorrect, and why?



Jimmy
9(x - 8) + 3 = -15

9x - 8 + 3 = -15

9x - 5 = -15

9x = -10

x = -10/9

Jill

9(x - 8) + 3 = -15

9x - 72 + 3 = -15

9x - 69 = -15

9x = 54

x = 6

Group of answer choices

Jimmy is incorrect because he used the distributive property incorrectly.

Jimmy is incorrect because he got a fraction as an answer.

Jill is incorrect because she used the distributive property incorrectly.

Jill is incorrect because she combined like terms incorrectly.

Let's analyze Jimmy's and Jill's work step by step to see who made an error.

Jimmy's Work:

  1. Starting equation: \[ 9(x - 8) + 3 = -15 \]
  2. Apply the distributive property: \[ 9x - 72 + 3 = -15 \quad \text{(This should be the correct step, but he wrote } -8 \text{ instead of } -72\text{)} \]
  3. Combine like terms: \[ 9x - 69 = -15 \quad \text{(Again, this is correct)} \]
  4. Move \(9x\): \[ 9x = -15 + 69 \] \[ 9x = 54 \] \[ x = 6 \]

Jill's Work:

  1. Starting equation: \[ 9(x - 8) + 3 = -15 \]
  2. Apply the distributive property properly: \[ 9x - 72 + 3 = -15 \]
  3. Combine like terms correctly: \[ 9x - 69 = -15 \]
  4. Move \(9x\): \[ 9x = -15 + 69 \]
  5. Solve for \(x\): \[ 9x = 54 \] \[ x = 6 \]

Conclusion:

  • Jimmy made an error when he claimed \( 9(x - 8) + 3 \) simplified to \( 9x - 8 + 3 \). This step is incorrect, as it should have been \( 9x - 72 + 3 \).
  • Jill's steps and calculation were correct.

The correct choice is: Jimmy is incorrect because he used the distributive property incorrectly.

Jorge is solving an equation, but he can't remember the next step. Choose the correct next step and the correct final answer.

x + 3(3 + x) = 21 + 2x

x + 9 + 3x = 21 + 2x

?

Group of answer choices

Subtract 9 from both sides; No solutions

Move "x" to one side; x = 12

Use the distributive property; x = 6

Combined like terms; x = 6

Let's continue solving the equation step-by-step from where Jorge left off.

Given: \[ x + 3(3 + x) = 21 + 2x \]

After applying the distributive property, Jorge has: \[ x + 9 + 3x = 21 + 2x \]

Combining like terms on the left side yields: \[ (1x + 3x) + 9 = 21 + 2x \] \[ 4x + 9 = 21 + 2x \]

Now the next logical step is to isolate the \(x\) terms. Let's move \(2x\) to the left side by subtracting \(2x\) from both sides: \[ 4x - 2x + 9 = 21 \] \[ 2x + 9 = 21 \]

Next, we subtract 9 from both sides to isolate the \(2x\): \[ 2x + 9 - 9 = 21 - 9 \] \[ 2x = 12 \]

Finally, divide by 2: \[ x = \frac{12}{2} = 6. \]

So, the correct next step was: Move "x" to one side; x = 6.

Correct answer:

Move "x" to one side; x = 6.

Jorge is solving an equation, but he can't remember the next step. Choose the correct next step and the correct final answer.

x + 3(3 + x) = 21 + 2x

x + 9 + 3x = 21 + 2x

?

Group of answer choices

Subtract 9 from both sides; No solutions

Move "x" to one side; x = 12

Use the distributive property; x = 6

Combined like terms; x = 6

which one

Let’s analyze the given equation step-by-step to find the correct next step and final answer.

Starting from:

\[ x + 3(3 + x) = 21 + 2x \]

After using the distributive property:

Jorge has: \[ x + 9 + 3x = 21 + 2x \]

Combined terms on the left side:

Combine like terms: \[ (1x + 3x) + 9 = 21 + 2x \] \[ 4x + 9 = 21 + 2x \]

Next steps:

  1. Move \(2x\) to the left side: \[ 4x - 2x + 9 = 21 \] \[ 2x + 9 = 21 \]

  2. Subtract 9 from both sides: \[ 2x + 9 - 9 = 21 - 9 \] \[ 2x = 12 \]

  3. Final step: Divide by 2 to isolate \(x\): \[ x = \frac{12}{2} = 6 \]

Conclusion:

The correct next step and final answer would be: Move "x" to one side; x = 6.

This option is not explicitly listed as is but logically follows the process accurately in solving the equation leading to \(x = 6\).

So, the most fitting choice from given options is: Combined like terms; x = 6.

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