Question

Make 'r' as the subject of the formula
m (n + r) = 5p

Answer 1

The equation written when r is the subject is:

`\displaystyle{r=(5p)/(m)-n}`

To make the term r as the subject of equation means to isolate r-term. In order to do that, we will apply properties of equality.

What are Properties of Equality?

Properties of equality are properties regarding equations/equality where states that when either sides are done by something (addition, subtraction, multiplication, division, etc.) then the other sides will also act the same as the acted side.

Example

Suppose we are given an equation of x = y. In this case, x and y are equal to each other. If x = 1 then y = 1. If we decide to add +2 to x we’d have to add it to y too so the result will be x + 2 = y + 2.

Same also applies to other equations!

Solution

Isolating r-term, first, we will apply division property where we divide both sides by m-term:

`\displaystyle{(m(n+r))/(m)=(5p)/(m)}\\\\\displaystyle{n+r=(5p)/(m)}`

Next, we use subtraction property to subtract both sides by n:

`\displaystyle{n+r-n=(5p)/(m)-n}\\\\\displaystyle{r=(5p)/(m)-n}`

Please let me know if you have any questions!