How to Solve Literal Equations

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Literal equations are formulas used to determine the value of a specific letter within an expression. Literal equations are used to determine interest, volume, pressure and other real-world applications. Unlike linear equations, where you simple solve to find the value of a variable, such as x, literal equations contain more unknown variables, such A = P(1 + r/n)^nt or P = 4s. The process of solving a literal equation is to find the value of one variable so that you can plug in the appropriate information and by using basic math skills, determine the value of the other variables.

Basic Process

  • Examine the following formula, rs = t. Solve for r.

    The question is asking you to get r by itself on one side of the equals sign . Do this by using the opposite mathematical property currently applied to the r, which in this case is multiplication.

  • Divide both sides of the equation by s. rs ÷ s = r and t ÷ s equals t/s. Therefore r = t/s. Which does not seem helpful at this point, but since the problem asked you to solve for r only, this is the correct solution.

  • Plug the information back into the problem to check your work or to continue solving if the problem asks for more information. (t/s)(s) = t. (t/s) x (s/1) = 1t and 1t = t, making the equation true, regardless of the numerical value of the variables.

Putting the Basic Process to Work

  • Read the following word problem. The perimeter of a rectangle is 190 feet. The width of the rectangle is 15 feet more than the length. What is the length of the rectangle?

  • Set up the formula to find the perimeter of a rectangle, which is P = 2L + 2W, or the perimeter equals twice the length plus twice the width. P = 2L + 2W is an example of a literal equation.

  • Plug in the information you know from the word problem. The perimeter or P = 190 feet and the width or W = L + 15. The formula now reads 190 = 2L + 2(L + 15).

  • Multiply the W formula first, 2 x L = 2L and 2 x 15 = 30. So W = 2L + 30. The equation reads 190 = 2L + 2L + 30.

  • Combine like terms, 2L + 2L = 4L, so that the formula reads 190 = 4L + 30.

  • Subtract 30 from both sides of the equation, 190 -- 30 = 4L + 30 -- 30, which simplifies to 160 = 4L.

  • Divide four from both sides of the equation, 160/4 = 4L/4, which simplifies to 40 = L.

  • Plug the value for L back into the equation to check your math 190 = 2(40) + 2(40 + 15). Solve and simplify. 190 = 80 + 110 or 190 = 190, which makes the equation true.

References

  • Photo Credit Thomas Northcut/Photodisc/Getty Images
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