Solved on Jan 23, 2024

Solve the linear equation $84x + 6 = 2(2x + 43)$ for $x$ .

STEP 1

Assumptions
1. We are given the equation $84x + 6 = 2(2x + 43)$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we will expand the right side of the equation by distributing the 2 across the terms inside the parentheses.
$84x + 6 = 2 \cdot 2x + 2 \cdot 43$

STEP 3

Perform the multiplication on the right side of the equation.
$84x + 6 = 4x + 86$

STEP 4

Next, we will subtract $4x$ from both sides of the equation to get all the $x$ terms on one side.
$84x + 6 - 4x = 4x + 86 - 4x$

STEP 5

Simplify both sides of the equation by combining like terms.
$80x + 6 = 86$

STEP 6

Now, we will subtract 6 from both sides of the equation to isolate the term with $x$ on one side.
$80x + 6 - 6 = 86 - 6$

STEP 7

Simplify both sides of the equation.
$80x = 80$

STEP 8

Finally, we will divide both sides of the equation by 80 to solve for $x$ .
$\frac{80x}{80} = \frac{80}{80}$

STEP 9

Simplify both sides of the equation to find the value of $x$ .
$x = 1$
The solution to the equation $84x + 6 = 2(2x + 43)$ is $x = 1$ .

Was this helpful?

Solve the linear equation $84x + 6 = 2(2x + 43)$ for $x$ .

STEP 1

Assumptions
1. We are given the equation $84x + 6 = 2(2x + 43)$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we will expand the right side of the equation by distributing the 2 across the terms inside the parentheses.
$84x + 6 = 2 \cdot 2x + 2 \cdot 43$

STEP 3

Perform the multiplication on the right side of the equation.
$84x + 6 = 4x + 86$

STEP 4

Next, we will subtract $4x$ from both sides of the equation to get all the $x$ terms on one side.
$84x + 6 - 4x = 4x + 86 - 4x$

STEP 5

Simplify both sides of the equation by combining like terms.
$80x + 6 = 86$

STEP 6

Now, we will subtract 6 from both sides of the equation to isolate the term with $x$ on one side.
$80x + 6 - 6 = 86 - 6$

STEP 7

Simplify both sides of the equation.
$80x = 80$

STEP 8

Finally, we will divide both sides of the equation by 80 to solve for $x$ .
$\frac{80x}{80} = \frac{80}{80}$

STEP 9

Simplify both sides of the equation to find the value of $x$ .
$x = 1$
The solution to the equation $84x + 6 = 2(2x + 43)$ is $x = 1$ .

Start learning now

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

Solve the linear equation 84x+6=2(2x+43)84x + 6 = 2(2x + 43)84x+6=2(2x+43) for xxx.

STEP 1

Assumptions1. We are given the equation 84x+6=2(2x+43)84x + 6 = 2(2x + 43)84x+6=2(2x+43).2. We need to solve for the variable xxx.

STEP 2

First, we will expand the right side of the equation by distributing the 2 across the terms inside the parentheses.84x+6=2⋅2x+2⋅4384x + 6 = 2 \cdot 2x + 2 \cdot 4384x+6=2⋅2x+2⋅43

STEP 3

Perform the multiplication on the right side of the equation.84x+6=4x+8684x + 6 = 4x + 8684x+6=4x+86

STEP 4

Next, we will subtract 4x4x4x from both sides of the equation to get all the xxx terms on one side.84x+6−4x=4x+86−4x84x + 6 - 4x = 4x + 86 - 4x84x+6−4x=4x+86−4x

STEP 5

Simplify both sides of the equation by combining like terms.80x+6=8680x + 6 = 8680x+6=86

STEP 6

Now, we will subtract 6 from both sides of the equation to isolate the term with xxx on one side.80x+6−6=86−680x + 6 - 6 = 86 - 680x+6−6=86−6

STEP 7

Simplify both sides of the equation.80x=8080x = 8080x=80

STEP 8

Finally, we will divide both sides of the equation by 80 to solve for xxx.80x80=8080\frac{80x}{80} = \frac{80}{80}8080x​=8080​

STEP 9

Simplify both sides of the equation to find the value of xxx.x=1x = 1x=1The solution to the equation 84x+6=2(2x+43)84x + 6 = 2(2x + 43)84x+6=2(2x+43) is x=1x = 1x=1.

Start learning now

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

Solve the linear equation $84x + 6 = 2(2x + 43)$ for $x$ .

Assumptions
1. We are given the equation $84x + 6 = 2(2x + 43)$ .
2. We need to solve for the variable $x$ .

First, we will expand the right side of the equation by distributing the 2 across the terms inside the parentheses.
$84x + 6 = 2 \cdot 2x + 2 \cdot 43$

Perform the multiplication on the right side of the equation.
$84x + 6 = 4x + 86$

Next, we will subtract $4x$ from both sides of the equation to get all the $x$ terms on one side.
$84x + 6 - 4x = 4x + 86 - 4x$

Simplify both sides of the equation by combining like terms.
$80x + 6 = 86$

Now, we will subtract 6 from both sides of the equation to isolate the term with $x$ on one side.
$80x + 6 - 6 = 86 - 6$

Simplify both sides of the equation.
$80x = 80$

Finally, we will divide both sides of the equation by 80 to solve for $x$ .
$\frac{80x}{80} = \frac{80}{80}$

Simplify both sides of the equation to find the value of $x$ .
$x = 1$
The solution to the equation $84x + 6 = 2(2x + 43)$ is $x = 1$ .