1. ## Multiplicative Inverse?

Solve $\displaystyle 3/4x - 5 = 4$

What I don't understand, is if I have to multiply each side by the reciprocal how do I do it if the reciprocal is infinite like 3/4, which ends up being 1.3333333 etc. etc.

2. $\displaystyle \begin{array}{rcl} \frac{3}{4}x - 5 & = & 4 \\ \frac{3}{4}x & = & 9 \\ \left( {\frac{4}{3}} \right)\frac{3}{4}x & = & 9\left( {\frac{4}{3}} \right) \\ x & = & 12 \\ \end{array}$

3. to obtain a reciprical, just switch the numerator and denominator.

the reciprical of 3/4 is 4/3

* the purpose of a reciprical is to get rid of any coefficients in front of your variable

so if you have 3/4 x -5 = 4

first you add 5 to both sides to get:

3/4 x = 9

now multiple by the reciprical of 3/4 which is 4/3

x = 12

try some practice problems...

find the reciprical of

1/12

34/2

0.5

0.1

NOTE: to find the recipricals of decimals you will first need to find its fractional equivalent.

the example you provided:

1.333333333333

its fraction is 4/3.

now swithc numerator and denominator to get 3/4

4. Originally Posted by Plato
$\displaystyle \begin{array}{rcl} \frac{3}{4}x - 5 & = & 4 \\ \frac{3}{4}x & = & 9 \\ \left( {\frac{4}{3}} \right)\frac{3}{4}x & = & 9\left( {\frac{4}{3}} \right) \\ x & = & 12 \\ \end{array}$
Thank you very much both of you for your help, it makes sense now.