Question

Solve each equation for $x$. $$\frac{x-1}{2 a}=2 x-a$$

   Solve each equation for $x$.
$$\frac{x-1}{2 a}=2 x-a$$

Precalculus Student Solutions Manual 5th

Precalculus Student Solutions Manual 5th

Margaret L. Lial,… 5th Edition

Chapter 1, Problem 54

Instant Answer

Solved by Expert Sarah X

08/04/2020

Step 1

Step 1: Multiply both sides of the equation by $2a$ to get rid of the fraction: $$2a \cdot \frac{x-1}{2 a}=2a \cdot (2 x-a)$$ This simplifies to: $$x-1=4ax-2a^2$$ Show more…

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Solve each equation for $x$. $$\frac{x-1}{2 a}=2 x-a$$

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Key Concepts

Rational Equations

A rational equation is an equation that involves one or more fractions whose numerators and/or denominators are expressions containing variables. Understanding rational equations is important for preventing potential domain issues like division by zero and for ensuring that any solution found is valid within the equation’s restrictions.

Clearing Fractions

Clearing fractions is a technique used to simplify equations that contain rational expressions. It involves multiplying both sides of the equation by the least common denominator (LCD) of all the fractions, thereby eliminating the fractions and reducing the equation to a form that can be more easily manipulated and solved.

Solving Linear Equations

Solving linear equations involves isolating the variable by performing inverse operations such as addition, subtraction, multiplication, or division on both sides of the equation. This fundamental skill in algebra allows for the systematic simplification of an equation to determine the value of the unknown variable.

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