Solved on Jan 17, 2024

Solve the linear equation $4x - 5 = -x$ for the unknown variable $x$ .

STEP 1

Assumptions
1. We have a linear equation in one variable: $4x - 5 = -x$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we want to isolate the variable $x$ on one side of the equation. To do this, we can add $x$ to both sides of the equation to move the term involving $x$ from the right side to the left side.
$4x - 5 + x = -x + x$

STEP 3

Combine like terms on both sides of the equation.
$4x + x - 5 = 0$

STEP 4

Simplify the left side by adding the coefficients of $x$ .
$5x - 5 = 0$

STEP 5

Next, we want to isolate $x$ completely. To do this, we can add $5$ to both sides of the equation to move the constant term from the left side to the right side.
$5x - 5 + 5 = 0 + 5$

STEP 6

Simplify both sides of the equation.
$5x = 5$

STEP 7

Now, to solve for $x$ , we divide both sides of the equation by the coefficient of $x$ , which is $5$ .
$\frac{5x}{5} = \frac{5}{5}$

STEP 8

Simplify both sides of the equation to find the value of $x$ .
$x = 1$
The solution to the equation $4x - 5 = -x$ is $x = 1$ .

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Solve the linear equation $4x - 5 = -x$ for the unknown variable $x$ .

STEP 1

Assumptions
1. We have a linear equation in one variable: $4x - 5 = -x$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we want to isolate the variable $x$ on one side of the equation. To do this, we can add $x$ to both sides of the equation to move the term involving $x$ from the right side to the left side.
$4x - 5 + x = -x + x$

STEP 3

Combine like terms on both sides of the equation.
$4x + x - 5 = 0$

STEP 4

Simplify the left side by adding the coefficients of $x$ .
$5x - 5 = 0$

STEP 5

Next, we want to isolate $x$ completely. To do this, we can add $5$ to both sides of the equation to move the constant term from the left side to the right side.
$5x - 5 + 5 = 0 + 5$

STEP 6

Simplify both sides of the equation.
$5x = 5$

STEP 7

Now, to solve for $x$ , we divide both sides of the equation by the coefficient of $x$ , which is $5$ .
$\frac{5x}{5} = \frac{5}{5}$

STEP 8

Simplify both sides of the equation to find the value of $x$ .
$x = 1$
The solution to the equation $4x - 5 = -x$ is $x = 1$ .

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Solve the linear equation 4x−5=−x4x - 5 = -x4x−5=−x for the unknown variable xxx.

STEP 1

Assumptions1. We have a linear equation in one variable: 4x−5=−x4x - 5 = -x4x−5=−x.2. We need to solve for the variable xxx.

STEP 2

First, we want to isolate the variable xxx on one side of the equation. To do this, we can add xxx to both sides of the equation to move the term involving xxx from the right side to the left side.4x−5+x=−x+x4x - 5 + x = -x + x4x−5+x=−x+x

STEP 3

Combine like terms on both sides of the equation.4x+x−5=04x + x - 5 = 04x+x−5=0

STEP 4

Simplify the left side by adding the coefficients of xxx.5x−5=05x - 5 = 05x−5=0

STEP 5

Next, we want to isolate xxx completely. To do this, we can add 555 to both sides of the equation to move the constant term from the left side to the right side.5x−5+5=0+55x - 5 + 5 = 0 + 55x−5+5=0+5

STEP 6

Simplify both sides of the equation.5x=55x = 55x=5

STEP 7

Now, to solve for xxx, we divide both sides of the equation by the coefficient of xxx, which is 555.5x5=55\frac{5x}{5} = \frac{5}{5}55x​=55​

STEP 8

Simplify both sides of the equation to find the value of xxx.x=1x = 1x=1The solution to the equation 4x−5=−x4x - 5 = -x4x−5=−x is x=1x = 1x=1.

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

Solve the linear equation $4x - 5 = -x$ for the unknown variable $x$ .

Assumptions
1. We have a linear equation in one variable: $4x - 5 = -x$ .
2. We need to solve for the variable $x$ .

First, we want to isolate the variable $x$ on one side of the equation. To do this, we can add $x$ to both sides of the equation to move the term involving $x$ from the right side to the left side.
$4x - 5 + x = -x + x$

Combine like terms on both sides of the equation.
$4x + x - 5 = 0$

Simplify the left side by adding the coefficients of $x$ .
$5x - 5 = 0$

Next, we want to isolate $x$ completely. To do this, we can add $5$ to both sides of the equation to move the constant term from the left side to the right side.
$5x - 5 + 5 = 0 + 5$

Simplify both sides of the equation.
$5x = 5$

Now, to solve for $x$ , we divide both sides of the equation by the coefficient of $x$ , which is $5$ .
$\frac{5x}{5} = \frac{5}{5}$

Simplify both sides of the equation to find the value of $x$ .
$x = 1$
The solution to the equation $4x - 5 = -x$ is $x = 1$ .