I am trying to help my daughter with her homework and feel like this is a foreign language. Can someone help. Here is one of the problems. If you can tell me how to solve it, I can figure out the rest of the problems.
x
___
2 = 7 and also
-1
___
8 p = 3
It greatly helps if you show division using /.
Is the first problem
\(\displaystyle x/2 = \dfrac{x}{2} = 7 \implies \frac{1}{2}x = 7.\)
The rule is to multiply both sides of the equation by the multiplicative inverse of the unknown's coefficient.
What does that mean in English?
\(\displaystyle 3u = 21.\) The multiplicative inverse of 3 is 1/3
\(\displaystyle \frac{1}{3} * 3u = \frac{1}{3} * 21 \implies\)
\(\displaystyle \dfrac{3u}{u} = \dfrac{21}{3} \implies\)
\(\displaystyle u = 7.\)
But our question involves a fractional coefficient. Same process. But what is the multiplicative inverse of a fraction. Just flip the fraction upside down.
\(\displaystyle x/2 = \dfrac{x}{2} = 7 \implies \frac{1}{2}x = 7.\) When I flip 1/2 upside down, I get 2/1 = 2.
\(\displaystyle x/2 = \frac{1}{2}x = 7 \implies 2 * \frac{1}{2}x = 2 * 7 \implies x = 14.\)
Is that clear or do you have questions. if you are OK here, let's go on to problem 2
