Ask a New Question
Menu

7. Solve this equation for y: 7y=12x

(1 point)
Responses

y=712x
y is equal to 7 over 12 x

y=12x+7
y is equal to 12 x plus 7

y=127x
y is equal to 12 sevenths x

y=12x−7
y is equal to 12 x minus 7
Question 2
8. Change the equation from standard form to slope-intercept form by solving for y.

8x−4y=24

Determine who changed the equation correctly:

Bob:

Subtract 8x from both sides: −4y=−8x+24

Divide by -4 on both sides: y=2x−6

Bill:

Subtract 8x from both sides: −4y=16x

Divide by -4 on both sides: y=−4x

Bud:

Subtract 8x from both sides: −4y=−8x+24

Divide by -4 on both sides: y=2x+24



(1 point)
Responses

Bob
Bob

Bill
Bill

Bud
Bud

None of them are correct
None of them are correct
Question 3
9. Solve 3x+2b=6c
for x.

Step 1: 3x+2b−2b=6c−2b
subtract 2b from both sides

Step 2: 3x=6c−2b
combine like terms/simplify

Step 3: 3x3=6c3−2b
divide by 3 on both sides to get x isolated

Step 4: x=2c−2b
simplify/final answer

Which statement is TRUE?

(1 point)
Responses

The process has an error. The correct answer is x=4bc3
The process has an error. The correct answer is x is equal to the fraction with numerator 4 b c and denominator 3

The process is correct.
The process is correct.

The process has an error. The correct answer is x=−4b−c
The process has an error. The correct answer is x is equal to negative 4 b minus c

The process has an error. The correct answer is x=2c−23b

1 answer

Let's analyze and answer each question step by step.

Question 1: Solve the equation for y: 7y = 12x

To solve for y, we divide both sides by 7: \[ y = \frac{12x}{7} \] This is the correct answer, which is equivalent to "y is equal to 12 over 7 x."

The closest response is:

  • y is equal to 12 over 7 x

Question 2: Change the equation from standard form to slope-intercept form by solving for y: 8x − 4y = 24

Let's check each person's work:

  • Bob:

    • Correct: Subtract 8x from both sides: \(-4y = -8x + 24\)
    • Correct: Divide by -4: \(y = 2x - 6\)

  • Bill:

    • Incorrect: When he subtracted \(8x\) from both sides, he incorrectly wrote \(-4y = 16x\)

  • Bud:

    • Incorrect: He starts correctly but incorrectly divides and writes it as \(y = 2x + 24\) instead of \(y = 2x - 6\).

Thus, Bob is the only one who changed the equation correctly, so the answer is:

  • Bob

Question 3: Solve 3x + 2b = 6c for x.

Let's analyze the steps:

  1. \(3x + 2b - 2b = 6c - 2b\) → Correct, this simplifies appropriately.
  2. \(3x = 6c - 2b\) → Correct, this is simplified properly.
  3. \(3x/3 = (6c - 2b)/3\) → Correctly dividing both sides by 3.
  4. \(x = 2c - \frac{2b}{3}\) → This is where there's a mistake in the final simplification.

The correct final answer should be: \[ x = 2c - \frac{2b}{3} \]

Thus, the statement "The process has an error. The correct answer is \(x = 2c - \frac{2b}{3}\)" is indeed true.

So the answer is:

  • The process has an error. The correct answer is \(x = 2c - \frac{2b}{3}\)

In summary:

  1. y is equal to 12 over 7 x
  2. Bob
  3. The process has an error. The correct answer is \(x = 2c - \frac{2b}{3}\)