Solved on Jan 18, 2024

Solve the linear equation $2+r=7+6r$ for the unknown variable $r$ .

STEP 1

Assumptions
1. We are given the linear equation $2 + r = 7 + 6r$ .
2. We need to solve for the variable $r$ .

STEP 2

To solve for $r$ , we need to isolate the variable on one side of the equation. We can start by subtracting $r$ from both sides to get the $r$ terms on one side.
$2 + r - r = 7 + 6r - r$

STEP 3

Simplify both sides of the equation by combining like terms.
$2 = 7 + 5r$

STEP 4

Next, we want to isolate the term with $r$ by moving the constant term on the right side to the left side. We do this by subtracting 7 from both sides of the equation.
$2 - 7 = 7 - 7 + 5r$

STEP 5

Simplify both sides of the equation.
$-5 = 5r$

STEP 6

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

STEP 7

Simplify both sides to get the value of $r$ .
$r = -1$
The solution to the equation $2 + r = 7 + 6r$ is $r = -1$ .

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Solve the linear equation $2+r=7+6r$ for the unknown variable $r$ .

STEP 1

Assumptions
1. We are given the linear equation $2 + r = 7 + 6r$ .
2. We need to solve for the variable $r$ .

STEP 2

To solve for $r$ , we need to isolate the variable on one side of the equation. We can start by subtracting $r$ from both sides to get the $r$ terms on one side.
$2 + r - r = 7 + 6r - r$

STEP 3

Simplify both sides of the equation by combining like terms.
$2 = 7 + 5r$

STEP 4

Next, we want to isolate the term with $r$ by moving the constant term on the right side to the left side. We do this by subtracting 7 from both sides of the equation.
$2 - 7 = 7 - 7 + 5r$

STEP 5

Simplify both sides of the equation.
$-5 = 5r$

STEP 6

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

STEP 7

Simplify both sides to get the value of $r$ .
$r = -1$
The solution to the equation $2 + r = 7 + 6r$ is $r = -1$ .

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Solve the linear equation 2+r=7+6r2+r=7+6r2+r=7+6r for the unknown variable rrr.

STEP 1

Assumptions1. We are given the linear equation 2+r=7+6r2 + r = 7 + 6r2+r=7+6r.2. We need to solve for the variable rrr.

STEP 2

To solve for rrr, we need to isolate the variable on one side of the equation. We can start by subtracting rrr from both sides to get the rrr terms on one side.2+r−r=7+6r−r2 + r - r = 7 + 6r - r2+r−r=7+6r−r

STEP 3

Simplify both sides of the equation by combining like terms.2=7+5r2 = 7 + 5r2=7+5r

STEP 4

Next, we want to isolate the term with rrr by moving the constant term on the right side to the left side. We do this by subtracting 7 from both sides of the equation.2−7=7−7+5r2 - 7 = 7 - 7 + 5r2−7=7−7+5r

STEP 5

Simplify both sides of the equation.−5=5r-5 = 5r−5=5r

STEP 6

Now, to solve for rrr, we divide both sides of the equation by the coefficient of rrr, which is 5.−55=5r5\frac{-5}{5} = \frac{5r}{5}5−5​=55r​

STEP 7

Simplify both sides to get the value of rrr.r=−1r = -1r=−1The solution to the equation 2+r=7+6r2 + r = 7 + 6r2+r=7+6r is r=−1r = -1r=−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 $2+r=7+6r$ for the unknown variable $r$ .

Assumptions
1. We are given the linear equation $2 + r = 7 + 6r$ .
2. We need to solve for the variable $r$ .

To solve for $r$ , we need to isolate the variable on one side of the equation. We can start by subtracting $r$ from both sides to get the $r$ terms on one side.
$2 + r - r = 7 + 6r - r$

Simplify both sides of the equation by combining like terms.
$2 = 7 + 5r$

Next, we want to isolate the term with $r$ by moving the constant term on the right side to the left side. We do this by subtracting 7 from both sides of the equation.
$2 - 7 = 7 - 7 + 5r$

Simplify both sides of the equation.
$-5 = 5r$

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

Simplify both sides to get the value of $r$ .
$r = -1$
The solution to the equation $2 + r = 7 + 6r$ is $r = -1$ .