Question Correct the error in the equation $2(x-4y)+3y=2x+11y$ . Choose the answer that fixes the error.

Studdy Solution

STEP 1

Assumptions
1. We are given an equation with a potential error in one of the operations.
2. We have four possible corrections to the equation.
3. We need to identify which correction will make the equation valid.

STEP 2

Let's start by expanding the left side of the original equation to see its simplified form.
$2(x-4y)+3y = 2x - 8y + 3y$

STEP 3

Combine like terms on the left side of the equation.
$2x - 8y + 3y = 2x - 5y$

STEP 4

Now, we have the simplified form of the left side of the equation:
$2x - 5y$

STEP 5

Next, we compare the simplified left side of the equation to the right side of the original equation to identify the error.
The original right side is:
$2x + 11y$

STEP 6

We can see that the coefficients of $x$ on both sides are the same, so the error must be in the coefficients of $y$ .

STEP 7

We need to find the correct operation that will make the coefficients of $y$ on both sides equal.

STEP 8

Let's test the first possible correction: Change $(x-4y)$ to $(x+4y)$ .
$2(x+4y)+3y = 2x + 8y + 3y$

STEP 9

Combine like terms for the first correction.
$2x + 8y + 3y = 2x + 11y$

STEP 10

Now, we compare the result of the first correction to the right side of the original equation.
$2x + 11y \stackrel{?}{=} 2x + 11y$

STEP 11

The first correction results in an equation where both sides are equal, which means it corrects the error.
$2x + 11y = 2x + 11y$
Therefore, changing $(x-4y)$ to $(x+4y)$ corrects the error in the equation.
The correct answer is: Change $(x-4y)$ to $(x+4y)$ .

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Question Correct the error in the equation $2(x-4y)+3y=2x+11y$ . Choose the answer that fixes the error.

Studdy Solution

STEP 1

Assumptions
1. We are given an equation with a potential error in one of the operations.
2. We have four possible corrections to the equation.
3. We need to identify which correction will make the equation valid.

STEP 2

Let's start by expanding the left side of the original equation to see its simplified form.
$2(x-4y)+3y = 2x - 8y + 3y$

STEP 3

Combine like terms on the left side of the equation.
$2x - 8y + 3y = 2x - 5y$

STEP 4

Now, we have the simplified form of the left side of the equation:
$2x - 5y$

STEP 5

Next, we compare the simplified left side of the equation to the right side of the original equation to identify the error.
The original right side is:
$2x + 11y$

STEP 6

We can see that the coefficients of $x$ on both sides are the same, so the error must be in the coefficients of $y$ .

STEP 7

We need to find the correct operation that will make the coefficients of $y$ on both sides equal.

STEP 8

Let's test the first possible correction: Change $(x-4y)$ to $(x+4y)$ .
$2(x+4y)+3y = 2x + 8y + 3y$

STEP 9

Combine like terms for the first correction.
$2x + 8y + 3y = 2x + 11y$

STEP 10

Now, we compare the result of the first correction to the right side of the original equation.
$2x + 11y \stackrel{?}{=} 2x + 11y$

STEP 11

The first correction results in an equation where both sides are equal, which means it corrects the error.
$2x + 11y = 2x + 11y$
Therefore, changing $(x-4y)$ to $(x+4y)$ corrects the error in the equation.
The correct answer is: Change $(x-4y)$ to $(x+4y)$ .

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Question Correct the error in the equation 2(x−4y)+3y=2x+11y2(x-4y)+3y=2x+11y2(x−4y)+3y=2x+11y. Choose the answer that fixes the error.

Studdy Solution

STEP 1

Assumptions1. We are given an equation with a potential error in one of the operations.2. We have four possible corrections to the equation.3. We need to identify which correction will make the equation valid.

STEP 2

Let's start by expanding the left side of the original equation to see its simplified form.2(x−4y)+3y=2x−8y+3y2(x-4y)+3y = 2x - 8y + 3y2(x−4y)+3y=2x−8y+3y

STEP 3

Combine like terms on the left side of the equation.2x−8y+3y=2x−5y2x - 8y + 3y = 2x - 5y2x−8y+3y=2x−5y

STEP 4

Now, we have the simplified form of the left side of the equation:2x−5y2x - 5y2x−5y

STEP 5

Next, we compare the simplified left side of the equation to the right side of the original equation to identify the error.The original right side is:2x+11y2x + 11y2x+11y

STEP 6

We can see that the coefficients of xxx on both sides are the same, so the error must be in the coefficients of yyy.

STEP 7

We need to find the correct operation that will make the coefficients of yyy on both sides equal.

STEP 8

Let's test the first possible correction: Change (x−4y)(x-4y)(x−4y) to (x+4y)(x+4y)(x+4y).2(x+4y)+3y=2x+8y+3y2(x+4y)+3y = 2x + 8y + 3y2(x+4y)+3y=2x+8y+3y

STEP 9

Combine like terms for the first correction.2x+8y+3y=2x+11y2x + 8y + 3y = 2x + 11y2x+8y+3y=2x+11y

STEP 10

Now, we compare the result of the first correction to the right side of the original equation.2x+11y=?2x+11y2x + 11y \stackrel{?}{=} 2x + 11y2x+11y=?2x+11y

STEP 11

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Question Correct the error in the equation $2(x-4y)+3y=2x+11y$ . Choose the answer that fixes the error.

Assumptions
1. We are given an equation with a potential error in one of the operations.
2. We have four possible corrections to the equation.
3. We need to identify which correction will make the equation valid.

Let's start by expanding the left side of the original equation to see its simplified form.
$2(x-4y)+3y = 2x - 8y + 3y$

Combine like terms on the left side of the equation.
$2x - 8y + 3y = 2x - 5y$

Now, we have the simplified form of the left side of the equation:
$2x - 5y$

Next, we compare the simplified left side of the equation to the right side of the original equation to identify the error.
The original right side is:
$2x + 11y$

We can see that the coefficients of $x$ on both sides are the same, so the error must be in the coefficients of $y$ .

We need to find the correct operation that will make the coefficients of $y$ on both sides equal.

Let's test the first possible correction: Change $(x-4y)$ to $(x+4y)$ .
$2(x+4y)+3y = 2x + 8y + 3y$

Combine like terms for the first correction.
$2x + 8y + 3y = 2x + 11y$

Now, we compare the result of the first correction to the right side of the original equation.
$2x + 11y \stackrel{?}{=} 2x + 11y$