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 Bud Bud Bob Bob None of them are correct None of them are correct Bill
The correct answer is Bob.
By subtracting 8x from both sides, Bob correctly gets -4y = -8x + 24.
Then, dividing by -4 on both sides, Bob correctly gets y = 2x - 6.
Both Bill and Bud made mistakes in their steps. Bill incorrectly gets y = -4x, and Bud incorrectly gets y = 2x + 24.
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=−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=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=2c−23b
The statement "The process is correct" is TRUE.
By subtracting 2b from both sides, the equation becomes 3x = 6c - 2b.
Then, by dividing both sides by 3, the equation correctly simplifies to x = (2c - 2b) / 3.
Therefore, the process is correct and the answer is x = (2c - 2b) / 3.
By subtracting 2b from both sides, the equation becomes 3x = 6c - 2b.
Then, by dividing both sides by 3, the equation correctly simplifies to x = (2c - 2b) / 3.
Bot GPT 3.5
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I THINK NOT
3x = 6c - 2b.
x = 2 c - (2/3) b
Apologies for the confusion. You are correct.
By subtracting 2b from both sides, the equation becomes 3x = 6c - 2b.
Then, by dividing both sides by 3, the equation simplifies to x = (6c - 2b) / 3.
My previous response was incorrect. The correct answer is x = (6c - 2b) / 3 or x = 2c - (2/3)b. Thank you for pointing out the error.
The correct answer is:
Bud
Bud correctly subtracts 8x from both sides:
-4y = -8x + 24
Next, Bud divides by -4 on both sides to isolate y:
y = 2x + 6
To change the equation from standard form to slope-intercept form, we need to solve for y. Let's go through each response and see who changed the equation correctly:
Bob's response:
Bob subtracted 8x from both sides correctly, obtaining -4y = -8x + 24. However, when dividing by -4 on both sides, Bob made a mistake by dividing 24 by -4 and obtaining -6 instead of -24/4 which is -6.
Bill's response:
Bill subtracted 8x from both sides correctly, obtaining -4y = 16x. However, when dividing by -4 on both sides, Bill made a mistake by not dividing 16x by -4. The correct step would be dividing both sides by -4: y = -4x.
Bud's response:
Bud subtracted 8x from both sides correctly, obtaining -4y = -8x + 24. When dividing by -4 on both sides, Bud correctly divided -8x and 24 by -4. The correct equation in slope-intercept form is y = 2x + 6.
Comparing the three responses, it is clear that Bud changed the equation correctly. Therefore, the correct response is Bud.