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QuestionSolve the equation: 5r+1520=3r−363\frac{5 r+15}{20}=\frac{3 r-36}{3}

Studdy Solution

STEP 1

Assumptions1. The given equation is 5r+1520=3r−363\frac{5 r+15}{20}=\frac{3 r-36}{3}

STEP 2

First, we will simplify both sides of the equation by reducing the fractions to their simplest form.On the left side, we can divide both the numerator and the denominator by5. On the right side, we can divide both the numerator and the denominator by.
5r+1520=r+4\frac{5 r+15}{20}=\frac{r+}{4}r−36=r−12\frac{ r-36}{}=r-12

STEP 3

Now, the simplified equation isr+3=r−12\frac{r+3}{}=r-12

STEP 4

Next, we will eliminate the fraction by multiplying both sides of the equation by4.
4⋅r+34=4⋅(r−12)4 \cdot \frac{r+3}{4}=4 \cdot (r-12)

STEP 5

This simplifies tor+3=4r−48r+3=4r-48

STEP 6

Now, we will isolate the variable rr on one side of the equation. We can do this by subtracting rr from both sides of the equation.
r+3−r=4r−48−rr+3-r=4r-48-r

STEP 7

This simplifies to3=3r−483=3r-48

STEP 8

Next, we will isolate rr by adding48 to both sides of the equation.
3+48=3r−48+483+48=3r-48+48

STEP 9

This simplifies to51=3r51=3r

STEP 10

Finally, we will solve for rr by dividing both sides of the equation by3.
513=r\frac{51}{3}=r

STEP 11

This simplifies tor=17r=17So, the solution to the equation is r=17r=17.

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