Question

remember, when solving multi-step equations it is important to show all steps every time. often, one persons thinking is a little different than anothers and a simple mistake is made... but they dont show all of the steps so we cant help them. please circle the step where the error is made (try to identify what they did). then, use the blank box on the right to resolve the entire problem, showing all of the steps.1. $7(y + 4.5) = 32.5$step 1 $7y + 4.5 = 32.5$step 2 $7y = 28$step 3 $y = 4LXB0-4(7j + 2) = 10$3. $3x^{2}+15 = 42$step 1 $3x^{2}= 57$step 2 $x^{2}= 19$step 3 $x = sqrt{19}LXB13(a + 7) = -33$

Explanation:

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Problem 1: $7(y + 4.5) = 32.5$

Step1: Identify error (Step1)

Original Step1 incorrectly distributed 7 only to $y$, not 4.5. Correct distribution:
$7y + 7\times4.5 = 32.5$
$7y + 31.5 = 32.5$

Step2: Subtract 31.5 from both sides

$7y = 32.5 - 31.5$
$7y = 1$

Step3: Divide by 7

$y = \frac{1}{7} \approx 0.14$

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Problem 2: $-4(7j + 2) = 10$

Step1: Identify error (Step1)

Original Step1 incorrectly multiplied 10 by -4 instead of dividing. Correct step: divide both sides by -4:
$7j + 2 = \frac{10}{-4}$
$7j + 2 = -2.5$

Step2: Subtract 2 from both sides

$7j = -2.5 - 2$
$7j = -4.5$

Step3: Divide by 7

$j = -\frac{4.5}{7} = -\frac{9}{14} \approx -0.64$

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Problem 3: $3x^2 +15 = 42$

Step1: Identify error (Step1)

Original Step1 added 15 to 42 instead of subtracting. Correct step: subtract 15 from both sides:
$3x^2 = 42 - 15$
$3x^2 = 27$

Step2: Divide by 3

$x^2 = \frac{27}{3}$
$x^2 = 9$

Step3: Take square root of both sides

$x = \pm\sqrt{9}$
$x = 3$ or $x = -3$

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Problem 4: $3(a + 7) = -33$

Step1: Identify error (Step2)

Original Step2 subtracted 7 incorrectly. Correct step: subtract 7 from both sides of $a + 7 = -11$:
$a = -11 - 7$
$a = -18$

Answer:

1. $y = \frac{1}{7}$
2. $j = -\frac{9}{14}$
3. $x = 3$ or $x = -3$
4. $a = -18$