Two less than three-fourths of a number is ten. What is the number?

Question:

Two less than three-fourths of a number is ten. What is the number?

Reverse Order of Operations

After constructing an equation, one can isolate a variable by undoing the order of operations associated with the variable.

Answer and Explanation:

{eq}\require{cancel} \begin{align} \frac{3}{4}x-2 &= 10\\ \frac{3}{4}x -2 +(2) &= 10 + (2) & \text{Add two to both sides.}\\ \frac{3}{4}x &= 12\\~\\ \frac{3}{1} \cdot \cancel{\frac{(4)}{4}}x &= 12 \cdot (4) &\text{Multiply four to both sides.}\\ 3x &= 48\\~\\ \cancel{\frac{3}{3}}x &= \frac{48}{3} & \text{Divide both sides by three.}\\ x &= \cancel{\frac{3}{3}}\cdot\frac{2\cdot2\cdot2\cdot2}{1}\\ x &= 16\\ \end{align} {/eq}


Learn more about this topic:

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Evaluating Simple Algebraic Expressions

from ELM: CSU Math Study Guide

Chapter 6 / Lesson 3
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