2.2: Literal Equations | Algebra 1 Honors

How it works

A literal equation contains more than one variable. Isolate the requested variable by treating the others as known quantities. Factoring can collect repeated appearances of the variable. State nonzero restrictions whenever division by an expression is needed.

A=\frac12bh\quad\Longrightarrow\quad h=\frac{2A}{b}\ (b\ne0)

Worked examples

Example 1

Solve $\displaystyle P=2l+2w$ for $\displaystyle w$ .

Subtract $\displaystyle 2l$ : $\displaystyle P-2l=2w$ . Divide by $\displaystyle 2$ : $\displaystyle w=P/2-l$ .

Example 2

Solve $\displaystyle y=mx+b$ for $\displaystyle x$ , assuming $\displaystyle m\ne0$ .

Subtract $\displaystyle b$ and divide by $\displaystyle m$ : $\displaystyle x=(y-b)/m$ .

Problems

Problem 2.2.1

Solve $\displaystyle C=2\pi r$ for $\displaystyle r$ .

Show worked solution

Divide by $\displaystyle 2\pi$ : $\displaystyle r=C/(2\pi)$ .

Problem 2.2.2

Solve $\displaystyle v=u+at$ for $\displaystyle t$ , assuming $\displaystyle a\ne0$ .

Show worked solution

Subtract $\displaystyle u$ and divide by $\displaystyle a$ : $\displaystyle t=(v-u)/a$ .

Problem 2.2.3

Solve $\displaystyle Q=ab+ac$ for $\displaystyle a$ and state the needed restriction.

Show worked solution

Factor: $\displaystyle Q=a(b+c)$ . Thus $\displaystyle a=Q/(b+c)$ when $\displaystyle b+c\ne0$ .

Lesson Problems PDF Solutions PDF Unit MCQ

How it works

Worked examples

Example 1

Example 2

Problems

Problem 2.2.1

Problem 2.2.2

Problem 2.2.3

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