Solved on Feb 29, 2024

Identify the error in Henry's steps to solve an equation: $-5(-x-1)+4x-1=49$ .

STEP 1

Assumptions
1. The equation to solve is $-5(-x-1)+4x-1=49$ .
2. We need to check each step for errors in the solution process provided by Henry.

STEP 2

Let's start by examining the first step of the solution, where Henry distributes $-5$ into the parentheses $(-x-1)$ .
$-5(-x-1)+4x-1=49$

STEP 3

Distribute $-5$ to both $-x$ and $-1$ .
$-5(-x) - 5(-1) + 4x - 1 = 49$

STEP 4

Calculate the products.
$5x + 5 + 4x - 1 = 49$

STEP 5

Compare the result from STEP_4 with Henry's second line.
Henry's line: $-5x - 5 + 4x - 1 = 49$
Correct line: $5x + 5 + 4x - 1 = 49$

STEP 6

Identify the error from the comparison.
The error is in the distribution step from line (1) to line (2); Henry incorrectly distributed the negative sign.

STEP 7

Explain the error.
Henry should have multiplied $-5$ by $-x$ to get $5x$ and $-5$ by $-1$ to get $+5$ , but he incorrectly multiplied $-5$ by $-x$ to get $-5x$ and $-5$ by $-1$ to get $-5$ .

STEP 8

Conclude the correct step and the error made.
The error is in the step from line (1) to line (2); Henry did not distribute the negative sign correctly. The correct distribution would result in $5x + 5$ instead of $-5x - 5$ .
The correct equation after proper distribution should be:
$5x + 5 + 4x - 1 = 49$

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Identify the error in Henry's steps to solve an equation: $-5(-x-1)+4x-1=49$ .

STEP 1

Assumptions
1. The equation to solve is $-5(-x-1)+4x-1=49$ .
2. We need to check each step for errors in the solution process provided by Henry.

STEP 2

Let's start by examining the first step of the solution, where Henry distributes $-5$ into the parentheses $(-x-1)$ .
$-5(-x-1)+4x-1=49$

STEP 3

Distribute $-5$ to both $-x$ and $-1$ .
$-5(-x) - 5(-1) + 4x - 1 = 49$

STEP 4

Calculate the products.
$5x + 5 + 4x - 1 = 49$

STEP 5

Compare the result from STEP_4 with Henry's second line.
Henry's line: $-5x - 5 + 4x - 1 = 49$
Correct line: $5x + 5 + 4x - 1 = 49$

STEP 6

Identify the error from the comparison.
The error is in the distribution step from line (1) to line (2); Henry incorrectly distributed the negative sign.

STEP 7

Explain the error.
Henry should have multiplied $-5$ by $-x$ to get $5x$ and $-5$ by $-1$ to get $+5$ , but he incorrectly multiplied $-5$ by $-x$ to get $-5x$ and $-5$ by $-1$ to get $-5$ .

STEP 8

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Identify the error in Henry's steps to solve an equation: −5(−x−1)+4x−1=49-5(-x-1)+4x-1=49−5(−x−1)+4x−1=49.

STEP 1

Assumptions1. The equation to solve is −5(−x−1)+4x−1=49-5(-x-1)+4x-1=49−5(−x−1)+4x−1=49.2. We need to check each step for errors in the solution process provided by Henry.

STEP 2

Let's start by examining the first step of the solution, where Henry distributes −5-5−5 into the parentheses (−x−1)(-x-1)(−x−1).−5(−x−1)+4x−1=49-5(-x-1)+4x-1=49−5(−x−1)+4x−1=49

STEP 3

Distribute −5-5−5 to both −x-x−x and −1-1−1.−5(−x)−5(−1)+4x−1=49-5(-x) - 5(-1) + 4x - 1 = 49−5(−x)−5(−1)+4x−1=49

STEP 4

Calculate the products.5x+5+4x−1=495x + 5 + 4x - 1 = 495x+5+4x−1=49

STEP 5

Compare the result from STEP_4 with Henry's second line.Henry's line: −5x−5+4x−1=49-5x - 5 + 4x - 1 = 49−5x−5+4x−1=49Correct line: 5x+5+4x−1=495x + 5 + 4x - 1 = 495x+5+4x−1=49

STEP 6

Identify the error from the comparison.The error is in the distribution step from line (1) to line (2); Henry incorrectly distributed the negative sign.

STEP 7

Explain the error.Henry should have multiplied −5-5−5 by −x-x−x to get 5x5x5x and −5-5−5 by −1-1−1 to get +5+5+5, but he incorrectly multiplied −5-5−5 by −x-x−x to get −5x-5x−5x and −5-5−5 by −1-1−1 to get −5-5−5.

STEP 8

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Identify the error in Henry's steps to solve an equation: $-5(-x-1)+4x-1=49$ .

Assumptions
1. The equation to solve is $-5(-x-1)+4x-1=49$ .
2. We need to check each step for errors in the solution process provided by Henry.

Let's start by examining the first step of the solution, where Henry distributes $-5$ into the parentheses $(-x-1)$ .
$-5(-x-1)+4x-1=49$

Distribute $-5$ to both $-x$ and $-1$ .
$-5(-x) - 5(-1) + 4x - 1 = 49$

Calculate the products.
$5x + 5 + 4x - 1 = 49$

Compare the result from STEP_4 with Henry's second line.
Henry's line: $-5x - 5 + 4x - 1 = 49$
Correct line: $5x + 5 + 4x - 1 = 49$

Identify the error from the comparison.
The error is in the distribution step from line (1) to line (2); Henry incorrectly distributed the negative sign.

Explain the error.
Henry should have multiplied $-5$ by $-x$ to get $5x$ and $-5$ by $-1$ to get $+5$ , but he incorrectly multiplied $-5$ by $-x$ to get $-5x$ and $-5$ by $-1$ to get $-5$ .