# Multiplicative Inverse?

• Dec 27th 2007, 11:07 AM
elliotfsl
Multiplicative Inverse?
Solve $3/4x - 5 = 4$

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.
• Dec 27th 2007, 11:17 AM
Plato
$\begin{array}{rcl}
\frac{3}{4}x - 5 & = & 4 \\
\frac{3}{4}x & = & 9 \\
\left( {\frac{4}{3}} \right)\frac{3}{4}x & = & 9\left( {\frac{4}{3}} \right) \\
x & = & 12 \\
\end{array}$
• Dec 27th 2007, 11:17 AM
DINOCALC09
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
• Dec 27th 2007, 11:43 AM
elliotfsl
Quote:

Originally Posted by Plato
$\begin{array}{rcl}
\frac{3}{4}x - 5 & = & 4 \\
\frac{3}{4}x & = & 9 \\
\left( {\frac{4}{3}} \right)\frac{3}{4}x & = & 9\left( {\frac{4}{3}} \right) \\
x & = & 12 \\
\end{array}$

Thank you very much both of you for your help, it makes sense now. :)