Question

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

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

Precalculus

Robert Blitzer 6th Edition

Chapter 0, Problem 16

Instant Answer

Solved by Expert James Kiss

08/18/2021

Step 1

The denominators are 5, 2, and 3. The least common multiple of these numbers is 30. So, we multiply each term by the appropriate factor to get the denominators to be 30. This gives us: $$6(3x) - 15(x-3) = 10(x+2)$$ Show more…

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

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Key Concepts

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. These equations graph as straight lines and the process of solving them involves finding the value of the variable that makes the equation true.

Clearing Fractions

Clearing fractions is a technique used to simplify equations that include fractional terms by multiplying every term in the equation by the least common denominator (LCD) of all fractions, eliminating denominators and transforming the equation into a simpler form.

Combining Like Terms

Combining like terms involves grouping terms with the same variable factors and summing their coefficients. This simplification is critical in reducing the complexity of an equation, making it easier to isolate and solve for the variable.

Balancing Equations

Balancing equations is the process of performing the same operation on both sides of an equation to maintain equality. This principle ensures that when terms are moved or simplified, the integrity of the equation is preserved, leading to the correct solution for the variable.

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