Literal Equation

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Literal Equation: meaning, method and solved example (Algebra 1) – Maths PDF

In short: A literal equation is an equation with several letters, often a formula, that you rearrange to solve for one chosen variable using the same steps as for numbers.

Algebra 1AlgebraA-CED.A.4

What is Literal Equation?

A literal equation mixes letters instead of mostly numbers, like \(A = \frac{1}{2}bh\) for a triangle’s area. Rearranging it means getting one letter alone on one side, so that you can compute it whenever the others are known.

Nothing new is allowed: use inverse operations on both sides, in reverse order of operations, and treat every other letter as if it were a number. The goal is a formula such as \(h = \frac{2A}{b}\).

How to spot it

  • A formula from science or geometry must be rewritten with a different letter by itself.
  • The instructions say solve for y, solve for h or isolate the variable.
  • An equation in standard form such as \(3x + 2y = 12\) must become \(y = \ldots\) before graphing.
  • You will plug in many different numbers and want one ready-to-use formula.

The method

  1. In the literal equation, circle the letter you must isolate; treat all other letters like ordinary numbers.
  2. Undo addition and subtraction first by doing the opposite on both sides.
  3. Undo multiplication and division next, dividing or multiplying the whole side.
  4. Write the final line with the target letter alone, then test it with simple numbers.
A = (1/2) b h2A = b hh = 2A / bmultiply both sides by 2divide both sides by b
Solving the triangle area formula for h in two moves.

Literal Equation: solved example

Problem

The formula \(F = \frac{9}{5}C + 32\) converts Celsius to Fahrenheit. Solve it for C, then find C when a Phoenix thermometer reads 113°F.

Solution

Subtract 32 from both sides: \(F – 32 = \frac{9}{5}C\). Multiply by \(\frac{5}{9}\): \(C = \frac{5}{9}(F – 32)\).

Now \(F = 113\): \(C = \frac{5}{9}(113 – 32) = \frac{5}{9}(81) = 45\). The reading is 45°C.

Try it

Question 1

Solve \(V = lwh\) for h.

Show the answer

Divide both sides by \(lw\): \(h = \frac{V}{lw}\).

Question 2

Solve \(3x + 2y = 12\) for y.

Show the answer

\(2y = 12 – 3x\), so \(y = 6 – \frac{3}{2}x\).

Literal Equation vs. Equation

An ordinary equation usually asks for a number, like \(2x + 5 = 17\), and ends with \(x = 6\). A literal equation asks for a rearranged formula and ends with a letter on one side and an expression on the other. The steps are the same, but the answer is an expression, not a single value.

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