Solve for x: 6x + 19 = x


Solve for x:

{eq}6x + 19 = x {/eq}


The principle behind transposing is that you are not changing the equation because what you do in one side of the equation is also done in the other side of the equation. If you add one on one side and add one on the other side, you are essentially just adding zero to the equation.

Answer and Explanation:

To solve for {eq}x {/eq}, we collect like terms and isolate {eq}x {/eq} on one side of the equation:

{eq}6x + 19 = x {/eq}

{eq}6x - x + 19 - 19 = x - x - 19 {/eq}

{eq}5x = - 19 {/eq}

Dividing both sides with {eq}5 {/eq}:

{eq}\displaystyle \frac{5x}{5} = \frac{-19}{5} {/eq}

{eq}\displaystyle x = \frac{-19}{5} {/eq}

Thus, {eq}\displaystyle x = -3 \frac{4}{5} {/eq}.

Learn more about this topic:

Evaluating Simple Algebraic Expressions

from ELM: CSU Math Study Guide

Chapter 6 / Lesson 3

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