Question

Solve each linear equation. $$5+\frac{x-2}{3}=\frac{x+3}{8}$$

   Solve each linear equation.
$$5+\frac{x-2}{3}=\frac{x+3}{8}$$

Precalculus

Robert Blitzer 6th Edition

Chapter 0, Problem 14

Instant Answer

Solved by Expert James Kiss

08/18/2021

Step 1

The common denominator of 3 and 8 is 24. So, we can rewrite the equation as follows: $$24(5)+8(x-2)=3(x+3)$$ Show more…

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Solve each linear equation. $$5+\frac{x-2}{3}=\frac{x+3}{8}$$

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Key Concepts

Linear Equations

Linear equations involve an unknown variable raised only to the first power and are typically expressed in the form ax + b = c. Solving these equations requires a sequence of algebraic steps to isolate the unknown variable on one side, utilizing operations such as addition, subtraction, multiplication, and division.

Clearing Fractions Using the Least Common Denominator

When an equation contains fractions, one effective technique is to eliminate the fractions by multiplying every term by the least common denominator (LCD) of all the fractions. This process simplifies the equation, making it easier to combine like terms and isolate the variable.

Combining Like Terms

Combining like terms is the process of adding or subtracting terms that have the same variable factors. By doing so, the equation is simplified, which helps in reducing complexity and makes subsequent isolation of the variable more straightforward.

Isolating the Variable

Isolating the variable involves manipulating the equation so that the variable appears on one side by itself. This is achieved through inverse operations, where each operation performed on one side is also applied to the other side, ultimately leading to the solution of the equation.

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