Literal Equations « Loop’s Algebra Weblog

Literal Equations

Follow the solutions to the following three equations.

EXAMPLE 1

$3x=12$

$\frac{3x}{3}=\frac{12}{3}$

$x=4$

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That was easy, right?

Now let’s look at what we would call a more general case of the same problem:

EXAMPLE 2

$ax=12$

$\frac{ax}{a}=\frac{12}{a}$

$x=\frac{12}{a}$

What are the similarities and differnces between the equations’ in examples 1 and 2?

EX 1: $3x=12$ EX 2: $ax=12$

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Not so bad? Now let’s look at the most general case of the first equation:

EXAMPLE 3

$ax=b$

$\frac{ax}{a}=\frac{b}{a}$

$x=\frac{b}{a}$

Do you see the similarities between all three examples?

EX 1: $3x=12$ EX 2: $ax=12$ EX 3: $ax=b$

The third example is what we call a LITERAL EQUATION because the numbers in example 1 have been replace with letters.

However, the method used to solve them is the same!

Example 3 is an example of solving the literal equation, $ax=b$ , for $x$ in terms of $a$ and $b$

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OK, let’s try a slightly more complicated case: (solve for $r$ )

Specific case: More General case:

$2r+3=7$ $ar+3=7$

Even more General case: The most General case (literal equation)

$ar+b=7$ $ar+b=c$