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Question Find the correct solution and error for the given equation. −7(4−r)=35-7(4-r) = 35. The solution is r=−9r = -9. The error is that the right side of the equation should be 6363 after dividing each side by −7-7.

Studdy Solution

STEP 1

Assumptions
1. We are given an incorrect solution to the equation −7(4−r)=35-7(4-r) = 35.
2. We need to find the correct solution to the equation.
3. We need to identify the error in the provided solution steps.

STEP 2

First, let's correctly distribute −7-7 to both terms inside the parentheses.
−7(4−r)=−7⋅4+7⋅r-7(4-r) = -7 \cdot 4 + 7 \cdot r

STEP 3

Now, perform the multiplication to simplify the left side of the equation.
−7⋅4+7⋅r=−28+7r-7 \cdot 4 + 7 \cdot r = -28 + 7r

STEP 4

We can see that the first error is in the distribution step. The correct distribution should result in −28+7r-28 + 7r, not −28−7r-28 - 7r as shown in the incorrect solution. This corresponds to error option D.

STEP 5

Now, let's solve the equation correctly using the proper distribution from STEP_3.
−28+7r=35-28 + 7r = 35

STEP 6

To isolate the term with rr, add 2828 to both sides of the equation.
−28+7r+28=35+28-28 + 7r + 28 = 35 + 28

STEP 7

Simplify both sides of the equation.
7r=637r = 63

STEP 8

Now, divide both sides of the equation by 77 to solve for rr.
7r7=637\frac{7r}{7} = \frac{63}{7}

STEP 9

Calculate the value of rr.
r=9r = 9
The correct solution to the equation is r=9r = 9.
The error in the provided solution is that the left side of the equation should be −28+7r-28 + 7r after distributing, which corresponds to option D.

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