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solve for each equation for the variable indicated 1. s+4t= r is s2. 3m-7m= p for m

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2 Answers

1. s + 4t = r, solve for s

Your goal is to get s = something, so isolate the s! Right now, your s is followed by "+ 4t."
To get s by itself, you want to get rid of 4t from the left-hand-side of your equation.
To that end, subtract 4t from each side of the equation. (thus keeping your equation "balanced")

(s + 4t) - 4t = r - 4t

s + 4t - 4t = r - 4t

s + 0 = r - 4t

s = r - 4t 

2. 3m - 7m = p, solve for m

Your goal is to get m = something, but you have more than just one m term.
In fact, you have 3 m's from which you are subtracting 7 m's!
That means you have "negative 4" m's. (algebraically speaking, since you can't have a negative number of things in real life)

-4m = p

Now at this point, many students make the mistake of adding 4 to each side. DON'T DO THAT! Why?
Well, what's going on between -4 and m? Are you adding them? Subtracting? Multiplying? Dividing?
Right, the operation that's not written, but implied, is multiplication. -4m is (-4)*(m). 
Hence, if you want to get rid of the -4 that's being multiplied to the m, you'll want to use multiplication or division to get rid of the -4, not addition or subtraction. 

This gives you two options:

1) divide each side by -4
2) multiply each side by -1/4 (because dividing by a number is the same as multiplying by the reciprocal of that number)

-4m = p

(-4*m)/(-4) = p/(-4)

m/1 = p/(-4)

m = - p/4

*note: - p/4 = -p/4 = p/-4 

1. s + 4t = r

To solve for s (get it on one side), we subtract 4t from both sides to get:

s = r - 4t

2.  3m-7m = p

Since 3m and 7m both contain an m, we can combine them.

3-7= -4 so -4m = p

To solve for m, divide both sides by -4

m = -p/4