Algebra 1 Literal Equations and Formulas Worksheet Solutions (PDF)

Algebra 1 math worksheet solutions: Literal Equations and Formulas – Maths PDF

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This literal equations answers for Algebra 1 covers literal equations and formulas (Common Core A-CED.A.4, A-REI.A.1), with a free PDF to print.

Literal equations answers (Algebra 1) – first page of the printable PDF

This answer key explains every problem on the literal equations worksheet. Final answers are in bold, and the lines above them show how each result was found. Use it to correct mistakes and to look for patterns in the errors you make most often.

Algebra 1 · Common Core State Standards: A-CED.A.4, A-REI.A.1

Literal equations answers: exercises 1 to 10

Exercise 1 – Distance formula

Divide both sides by \(r\).

\(t = \frac{d}{r}\)

Exercise 2 – Perimeter of a square

Divide both sides by 4.

\(s = \frac{P}{4}\)

Exercise 3 – Area of a rectangle

Divide both sides by \(l\).

\(w = \frac{A}{l}\)

Exercise 4 – Circumference

Divide both sides by \(2\pi\).

\(r = \frac{C}{2\pi}\)

Exercise 5 – Solve for b

Subtract \(mx\) from both sides.

\(b = y – mx\)

Exercise 6 – Solve for x

Subtract \(b\): \(y – b = mx\).

Divide by \(m\).

\(x = \frac{y – b}{m}\)

Exercise 7 – Perimeter of a rectangle

Subtract \(2w\): \(P – 2w = 2l\).

Divide by 2.

\(l = \frac{P – 2w}{2}\)

Exercise 8 – Area of a triangle

Isolating h.

Multiply both sides by 2: \(2A = bh\).

Divide by \(b\).

\(h = \frac{2A}{b}\)

Exercise 9 – Temperature formula

Subtract 32: \(F – 32 = \frac{9}{5}C\).

Multiply by \(\frac{5}{9}\).

\(C = \frac{5}{9}(F – 32)\)

Exercise 10 – Volume of a prism

Divide both sides by \(lw\).

\(h = \frac{V}{lw}\)

Exercises 11 and up

Exercise 11 – General linear form

Subtract \(b\): \(ax = c – b\).

Divide by \(a\).

\(x = \frac{c – b}{a}\)

Exercise 12 – Standard form to slope-intercept

Subtract \(3x\): \(2y = 12 – 3x\).

Divide every term by 2.

\(y = 6 – \frac{3}{2}x\)

Exercise 13 – Variable on both sides

Subtract \(cx\) and \(b\): \(ax – cx = d – b\).

Factor: \(x(a – c) = d – b\).

Divide by \(a – c\).

\(x = \frac{d – b}{a – c}\)

Exercise 14 – Surface area of a cylinder

Subtract \(2\pi r^{2}\): \(S – 2\pi r^{2} = 2\pi rh\).

Divide by \(2\pi r\).

\(h = \frac{S – 2\pi r^{2}}{2\pi r}\)

Exercise 15 – Trapezoid

Top base 12 gives area 60.

Multiply by 2: \(2A = (b_{1} + b_{2})h\). Divide by \(h\): \(\frac{2A}{h} = b_{1} + b_{2}\).

Subtract \(b_{2}\): \(b_{1} = \frac{2A}{h} – b_{2}\).

Substitute: \(b_{1} = \frac{2(60)}{6} – 8 = 20 – 8 = 12\).

\(b_{1} = \frac{2A}{h} – b_{2}\); \(b_{1} = 12\)

Exercise 16 – Simple interest

Divide by \(Pr\): \(t = \frac{I}{Pr}\).

Substitute: \(t = \frac{180}{1500(0.04)} = \frac{180}{60} = 3\).

\(t = \frac{I}{Pr}\); 3 years

Exercise 17 – Convert a temperature

Substitute: \(C = \frac{5}{9}(77 – 32) = \frac{5}{9}(45)\).

Multiply: \(C = 25\).

25°C

Exercise 18 – Fence length

Length 14 feet.

\(l = \frac{P – 2w}{2}\).

Substitute: \(l = \frac{46 – 2(9)}{2} = \frac{28}{2} = 14\).

\(l = \frac{P – 2w}{2}\); 14 feet

Exercise 19 – Road trip speed

Divide by \(t\): \(r = \frac{d}{t}\).

Substitute: \(r = \frac{330}{5.5} = 60\).

\(r = \frac{d}{t}\); 60 mph

Exercise 20 – Slope formula

Multiply by \(x_{2} – x_{1}\): \(m(x_{2} – x_{1}) = y_{2} – y_{1}\).

Add \(y_{1}\): \(y_{2} = m(x_{2} – x_{1}) + y_{1}\).

Substitute: \(y_{2} = 3(5 – 1) + 2 = 14\).

\(y_{2} = m(x_{2} – x_{1}) + y_{1}\); \(y_{2} = 14\)

Exercise 21 – Soup can

Divide by \(\pi r^{2}\): \(h = \frac{V}{\pi r^{2}}\).

Substitute: \(h = \frac{90\pi}{\pi (3)^{2}} = \frac{90\pi}{9\pi} = 10\).

\(h = \frac{V}{\pi r^{2}}\); 10 inches

Key facts behind this literal equations answers

Key facts

A literal equation contains two or more variables, like a formula.
Solve for a variable by applying inverse operations to both sides.
Treat the other letters as if they were numbers.
When the variable appears in two terms, collect those terms and factor.
The answer is an expression, not necessarily a number.

How to use this literal equations answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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