Question

Solve each equation. $$ \frac{x}{5}+\frac{3 x-1}{2}=\frac{6 x+5}{4} $$

   Solve each equation.
$$
\frac{x}{5}+\frac{3 x-1}{2}=\frac{6 x+5}{4}
$$

Precalculus

Raymond A. Barnett,… 7th Edition

Chapter 1, Problem 18

Instant Answer

Solved by Expert Erika Bustos

07/17/2021

Step 1

The common denominator is 20. So, we multiply the entire equation by 20 to eliminate the fractions: \[ 20 \cdot \frac{x}{5} + 20 \cdot \frac{3x-1}{2} = 20 \cdot \frac{6x+5}{4} \] Show more…

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Solve each equation. $$ \frac{x}{5}+\frac{3 x-1}{2}=\frac{6 x+5}{4} $$

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Key Concepts

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves combining like terms, distributing, and factoring where necessary to rewrite the equation in a more manageable form. This process is essential for reducing complex expressions and isolating the variable to find the solution.

Least Common Multiple (LCM)

The least common multiple of denominators is used to find a common factor that can be multiplied across all terms in an equation to eliminate fractions. It is a crucial concept when working with equations that contain multiple fractional terms.

Linear Equations

Linear equations involve expressions that set two algebraic expressions equal, typically resulting in a solution that makes both sides equal when substituted back into the equation. They are fundamental to algebra and arise in various contexts, from simple problems to complex systems.

Clearing Fractions

Clearing fractions involves multiplying each term in an equation by a common denominator to eliminate fractions, making the equation easier to solve. This technique simplifies the equation by converting it into an equivalent form without fractional coefficients.

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