Solved on Mar 11, 2024

Solve the linear equation $6x - 68 = 2x - 44$ for $x$ .

STEP 1

Assumptions
1. We are given a linear equation in one variable $x$ .
2. The equation is $6x - 68 = 2x - 44$ .
3. We need to solve for $x$ .

STEP 2

First, we will collect all the terms containing $x$ on one side of the equation. To do this, we will subtract $2x$ from both sides of the equation.
$6x - 68 - 2x = 2x - 44 - 2x$

STEP 3

Simplify both sides of the equation by combining like terms.
$(6x - 2x) - 68 = -44$

STEP 4

Calculate the difference of the $x$ terms.
$4x - 68 = -44$

STEP 5

Next, we will isolate the term containing $x$ by adding $68$ to both sides of the equation to move the constant term to the right side.
$4x - 68 + 68 = -44 + 68$

STEP 6

Simplify both sides of the equation by performing the addition.
$4x = 24$

STEP 7

Now, we need to solve for $x$ . To do this, we will divide both sides of the equation by $4$ to isolate $x$ .
$\frac{4x}{4} = \frac{24}{4}$

STEP 8

Calculate the division to find the value of $x$ .
$x = 6$
The solution to the equation $6x - 68 = 2x - 44$ is $x = 6$ .

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Solve the linear equation $6x - 68 = 2x - 44$ for $x$ .

STEP 1

Assumptions
1. We are given a linear equation in one variable $x$ .
2. The equation is $6x - 68 = 2x - 44$ .
3. We need to solve for $x$ .

STEP 2

First, we will collect all the terms containing $x$ on one side of the equation. To do this, we will subtract $2x$ from both sides of the equation.
$6x - 68 - 2x = 2x - 44 - 2x$

STEP 3

Simplify both sides of the equation by combining like terms.
$(6x - 2x) - 68 = -44$

STEP 4

Calculate the difference of the $x$ terms.
$4x - 68 = -44$

STEP 5

Next, we will isolate the term containing $x$ by adding $68$ to both sides of the equation to move the constant term to the right side.
$4x - 68 + 68 = -44 + 68$

STEP 6

Simplify both sides of the equation by performing the addition.
$4x = 24$

STEP 7

Now, we need to solve for $x$ . To do this, we will divide both sides of the equation by $4$ to isolate $x$ .
$\frac{4x}{4} = \frac{24}{4}$

STEP 8

Calculate the division to find the value of $x$ .
$x = 6$
The solution to the equation $6x - 68 = 2x - 44$ is $x = 6$ .

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Solve the linear equation 6x−68=2x−446x - 68 = 2x - 446x−68=2x−44 for xxx.

STEP 1

Assumptions1. We are given a linear equation in one variable xxx.2. The equation is 6x−68=2x−446x - 68 = 2x - 446x−68=2x−44.3. We need to solve for xxx.

STEP 2

First, we will collect all the terms containing xxx on one side of the equation. To do this, we will subtract 2x2x2x from both sides of the equation.6x−68−2x=2x−44−2x6x - 68 - 2x = 2x - 44 - 2x6x−68−2x=2x−44−2x

STEP 3

Simplify both sides of the equation by combining like terms.(6x−2x)−68=−44(6x - 2x) - 68 = -44(6x−2x)−68=−44

STEP 4

Calculate the difference of the xxx terms.4x−68=−444x - 68 = -444x−68=−44

STEP 5

Next, we will isolate the term containing xxx by adding 686868 to both sides of the equation to move the constant term to the right side.4x−68+68=−44+684x - 68 + 68 = -44 + 684x−68+68=−44+68

STEP 6

Simplify both sides of the equation by performing the addition.4x=244x = 244x=24

STEP 7

Now, we need to solve for xxx. To do this, we will divide both sides of the equation by 444 to isolate xxx.4x4=244\frac{4x}{4} = \frac{24}{4}44x​=424​

STEP 8

Calculate the division to find the value of xxx.x=6x = 6x=6The solution to the equation 6x−68=2x−446x - 68 = 2x - 446x−68=2x−44 is x=6x = 6x=6.

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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 $6x - 68 = 2x - 44$ for $x$ .

Assumptions
1. We are given a linear equation in one variable $x$ .
2. The equation is $6x - 68 = 2x - 44$ .
3. We need to solve for $x$ .

First, we will collect all the terms containing $x$ on one side of the equation. To do this, we will subtract $2x$ from both sides of the equation.
$6x - 68 - 2x = 2x - 44 - 2x$

Simplify both sides of the equation by combining like terms.
$(6x - 2x) - 68 = -44$

Calculate the difference of the $x$ terms.
$4x - 68 = -44$

Next, we will isolate the term containing $x$ by adding $68$ to both sides of the equation to move the constant term to the right side.
$4x - 68 + 68 = -44 + 68$

Simplify both sides of the equation by performing the addition.
$4x = 24$

Now, we need to solve for $x$ . To do this, we will divide both sides of the equation by $4$ to isolate $x$ .
$\frac{4x}{4} = \frac{24}{4}$

Calculate the division to find the value of $x$ .
$x = 6$
The solution to the equation $6x - 68 = 2x - 44$ is $x = 6$ .