Solve literal equations and simultaneous literal equations

Solve literal equations and simultaneous literal equations

A literal equation contains parameters whose values may vary. Treat the parameters as constants while isolating the target variable, and state any condition needed for division

1. Treat parameters as constants Letters other than the target variable stay as fixed quantities during the rearrangement \(\displaystyle 3x+2a=5b\)
2. Apply operations to both sides Move a non-target term by performing the same inverse operation on each side \(\displaystyle 3x+2a=5b\Rightarrow3x=5b-2a\)
3. Divide by the whole coefficient The complete coefficient of the target variable divides the entire other side \(\displaystyle 3x=5b-2a\Rightarrow x=\frac{5b-2a}{3}\)
4. State non-zero restrictions A denominator or coefficient used for division must not be zero \(\displaystyle x=\frac{C-B}{A},\quad A\ne0\)

Worked example

Make x the subject of the literal equation, assuming p is non-zero

1. \(\displaystyle px+2q=3r\)The target variable x is multiplied by p and the non-target term is 2q
2. \(\displaystyle px=3r-2q\)Subtract 2q from both sides
3. \(\displaystyle x=\frac{3r-2q}{p},\quad p\ne0\)Divide the whole right side by p and state the division restriction
4. \(\displaystyle p\left(\frac{3r-2q}{p}\right)+2q=3r\)Substitution into the original equation verifies the rearranged formula when p is non-zero

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