Question

Solve each equation. $$\frac{q}{6}+1-3 q=2-4 q+\frac{q}{8}$$

   Solve each equation.
$$\frac{q}{6}+1-3 q=2-4 q+\frac{q}{8}$$

Precalculus

John W. Coburn 2nd Edition

Chapter 1, Problem 30

Instant Answer

Solved by Expert Jake Zanazzi

05/17/2020

Step 1

On the left side, we have $\frac{q}{6}$ and $-3q$, and on the right side, we have $-4q$ and $\frac{q}{8}$. Show more…

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Solve each equation. $$\frac{q}{6}+1-3 q=2-4 q+\frac{q}{8}$$

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Key Concepts

Properties of Equality

Properties of equality allow the same operation to be performed on both sides of an equation without changing its balance. This concept is critical for manipulating equations, such as adding, subtracting, multiplying, or dividing both sides by the same number, to ultimately solve for the variable.

Combining Like Terms

Combining like terms involves merging terms with identical variable parts to simplify an equation. This process reduces the equation to fewer terms, making it easier to isolate the variable.

Linear Equations

A linear equation is an equation in which the variable appears only to the first power and there are no products of variables. Solving a linear equation involves isolating the variable by performing operations such as addition, subtraction, multiplication, and division.

Equations with Fractions

Equations that include fractions require special handling to simplify the solving process. Multiplying both sides of the equation by the least common denominator eliminates fractions and converts the equation into a simpler form that is easier to work with.

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