QuestionSolve. $\frac{5 r+10}{15}=\frac{2 r-8}{2}$
The solution is $\mathrm{r}=$ $\square$ (Simplify your answer.)

Studdy Solution

STEP 1

1. The equation $\frac{5r+10}{15} = \frac{2r-8}{2}$ is a rational equation.
2. We need to solve for the variable $r$ .
3. The equation involves fractions, so we will need to eliminate the fractions to simplify the equation.

STEP 2

1. Eliminate the fractions by finding a common denominator or by cross-multiplying.
2. Simplify the resulting equation.
3. Solve for $r$ .
4. Check the solution by substituting it back into the original equation.

STEP 3

To eliminate the fractions, we can cross-multiply. This means multiplying the numerator of each fraction by the denominator of the other fraction:
$(5r + 10) \cdot 2 = (2r - 8) \cdot 15$

STEP 4

Distribute the multiplication on both sides:
Left side: $2 \cdot (5r + 10) = 10r + 20$
Right side: $15 \cdot (2r - 8) = 30r - 120$

STEP 5

Now, we have the equation: $10r + 20 = 30r - 120$

STEP 6

To solve for $r$ , first move all terms involving $r$ to one side and constant terms to the other side. Subtract $10r$ from both sides:
$20 = 30r - 10r - 120$
This simplifies to:
$20 = 20r - 120$

STEP 7

Add 120 to both sides to isolate terms with $r$ :
$20 + 120 = 20r$
$140 = 20r$

STEP 8

Divide both sides by 20 to solve for $r$ :
$r = \frac{140}{20}$
Simplify the fraction:
$r = 7$

STEP 9

Check the solution by substituting $r = 7$ back into the original equation:
Left side: $\frac{5(7) + 10}{15} = \frac{35 + 10}{15} = \frac{45}{15} = 3$
Right side: $\frac{2(7) - 8}{2} = \frac{14 - 8}{2} = \frac{6}{2} = 3$
Both sides are equal, confirming that the solution is correct.
The solution is: $\mathrm{r} = \boxed{7}$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

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

Parents Influencer program Contact Policy Terms