Solved on Feb 22, 2024

Solve the equation $7x - (5x - 1) = 2$ and express the answer as an integer or simplified fraction.

STEP 1

Assumptions
1. We have the equation $7x - (5x - 1) = 2$ .
2. We need to solve for $x$ .
3. The solution should be expressed as an integer or simplified fraction.

STEP 2

First, we need to simplify the left side of the equation by distributing the negative sign inside the parentheses.
$7x - (5x - 1) = 7x - 5x + 1$

STEP 3

Combine like terms on the left side of the equation.
$7x - 5x + 1 = 2x + 1$

STEP 4

Now, we need to isolate the variable $x$ on one side of the equation. To do this, we subtract 1 from both sides of the equation.
$2x + 1 - 1 = 2 - 1$

STEP 5

Simplify both sides of the equation after the subtraction.
$2x = 1$

STEP 6

To solve for $x$ , divide both sides of the equation by 2.
$\frac{2x}{2} = \frac{1}{2}$

STEP 7

Simplify the equation to find the value of $x$ .
$x = \frac{1}{2}$
The solution to the equation $7x - (5x - 1) = 2$ is $x = \frac{1}{2}$ .

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Solve the equation $7x - (5x - 1) = 2$ and express the answer as an integer or simplified fraction.

STEP 1

Assumptions
1. We have the equation $7x - (5x - 1) = 2$ .
2. We need to solve for $x$ .
3. The solution should be expressed as an integer or simplified fraction.

STEP 2

First, we need to simplify the left side of the equation by distributing the negative sign inside the parentheses.
$7x - (5x - 1) = 7x - 5x + 1$

STEP 3

Combine like terms on the left side of the equation.
$7x - 5x + 1 = 2x + 1$

STEP 4

Now, we need to isolate the variable $x$ on one side of the equation. To do this, we subtract 1 from both sides of the equation.
$2x + 1 - 1 = 2 - 1$

STEP 5

Simplify both sides of the equation after the subtraction.
$2x = 1$

STEP 6

To solve for $x$ , divide both sides of the equation by 2.
$\frac{2x}{2} = \frac{1}{2}$

STEP 7

Simplify the equation to find the value of $x$ .
$x = \frac{1}{2}$
The solution to the equation $7x - (5x - 1) = 2$ is $x = \frac{1}{2}$ .

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Solve the equation 7x−(5x−1)=27x - (5x - 1) = 27x−(5x−1)=2 and express the answer as an integer or simplified fraction.

STEP 1

Assumptions1. We have the equation 7x−(5x−1)=27x - (5x - 1) = 27x−(5x−1)=2.2. We need to solve for xxx.3. The solution should be expressed as an integer or simplified fraction.

STEP 2

First, we need to simplify the left side of the equation by distributing the negative sign inside the parentheses.7x−(5x−1)=7x−5x+17x - (5x - 1) = 7x - 5x + 17x−(5x−1)=7x−5x+1

STEP 3

Combine like terms on the left side of the equation.7x−5x+1=2x+17x - 5x + 1 = 2x + 17x−5x+1=2x+1

STEP 4

Now, we need to isolate the variable xxx on one side of the equation. To do this, we subtract 1 from both sides of the equation.2x+1−1=2−12x + 1 - 1 = 2 - 12x+1−1=2−1

STEP 5

Simplify both sides of the equation after the subtraction.2x=12x = 12x=1

STEP 6

To solve for xxx, divide both sides of the equation by 2.2x2=12\frac{2x}{2} = \frac{1}{2}22x​=21​

STEP 7

Simplify the equation to find the value of xxx.x=12x = \frac{1}{2}x=21​The solution to the equation 7x−(5x−1)=27x - (5x - 1) = 27x−(5x−1)=2 is x=12x = \frac{1}{2}x=21​.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve the equation $7x - (5x - 1) = 2$ and express the answer as an integer or simplified fraction.

Assumptions
1. We have the equation $7x - (5x - 1) = 2$ .
2. We need to solve for $x$ .
3. The solution should be expressed as an integer or simplified fraction.

First, we need to simplify the left side of the equation by distributing the negative sign inside the parentheses.
$7x - (5x - 1) = 7x - 5x + 1$

Combine like terms on the left side of the equation.
$7x - 5x + 1 = 2x + 1$

Now, we need to isolate the variable $x$ on one side of the equation. To do this, we subtract 1 from both sides of the equation.
$2x + 1 - 1 = 2 - 1$

Simplify both sides of the equation after the subtraction.
$2x = 1$

To solve for $x$ , divide both sides of the equation by 2.
$\frac{2x}{2} = \frac{1}{2}$

Simplify the equation to find the value of $x$ .
$x = \frac{1}{2}$
The solution to the equation $7x - (5x - 1) = 2$ is $x = \frac{1}{2}$ .