Question

Solve the equations. $$\frac{5}{4} x=\frac{5}{6} x+\frac{2}{3}$$

   Solve the equations.
$$\frac{5}{4} x=\frac{5}{6} x+\frac{2}{3}$$

Prealgebra

Julie Miller, Molly… 1st Edition

Chapter 4, Problem 69

Instant Answer

Solved by Expert Erin Kearney

07/31/2020

Step 1

This gives us: $$12 \cdot \frac{5}{4} x = 12 \cdot \frac{5}{6} x + 12 \cdot \frac{2}{3}$$ which simplifies to: $$15x = 10x + 8$$ Show more…

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Solve the equations. $$\frac{5}{4} x=\frac{5}{6} x+\frac{2}{3}$$

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Key Concepts

Clearing Fractions

Clearing fractions involves multiplying all terms in an equation by a common denominator, often the least common denominator (LCD), to eliminate fractional terms and simplify the equation. This method makes it easier to isolate the variable.

Properties of Equality

The properties of equality allow for the same operation to be performed on both sides of an equation without affecting the balance of the equation. These properties are critical when rearranging terms, combining like terms, or isolating variables.

Linear Equations

A linear equation is an equation where the variable appears with an exponent of one and the graph of the equation forms a straight line. Solving these equations involves finding the value of the variable that makes the equation true.

Manipulating Fractions

Manipulating fractions includes operations such as addition, subtraction, multiplication, and division of fractional expressions. This is essential when fractions appear in equations, ensuring that they are correctly combined or simplified.

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