Question

Solve: $\frac{5}{2} x-1 \geq x+\frac{4}{5}$

   Solve: $\frac{5}{2} x-1 \geq x+\frac{4}{5}$

College Algebra

College Algebra

Michael Sullivan 11th Edition

Chapter 8, Problem 66

Instant Answer

Solved by Expert Nicole Hoffman

02/27/2023

Step 1

This gives us: \[\frac{5}{2}x - x - 1 \geq \frac{4}{5}\] which simplifies to: \[\frac{3}{2}x - 1 \geq \frac{4}{5}\] Show more…

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Solve: $\frac{5}{2} x-1 \geq x+\frac{4}{5}$

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Key Concepts

Linear Inequalities

This concept involves inequalities that contain linear expressions on one or both sides. Understanding linear inequalities is essential because they describe ranges of values for variables that satisfy a given condition, and they are solved using methods similar to those for linear equations, with extra attention paid to the direction of the inequality sign.

Algebraic Manipulation

Algebraic manipulation is the process of rearranging and simplifying equations or inequalities to isolate the variable of interest. This includes adding, subtracting, multiplying, or dividing terms on both sides, and is fundamental to solving many mathematical problems, including solving inequalities.

Operations with Fractions

Working with fractions involves finding common denominators, simplifying expressions, and performing arithmetic operations on fractional expressions. Mastery of this concept is important when dealing with equations or inequalities that include fractional coefficients and constants, enabling the transformation of the problem into a more manageable form.

Properties of Inequalities

The properties of inequalities, such as the rules that govern the direction of an inequality when both sides are multiplied or divided by a negative number, are crucial for correctly solving inequality problems. These properties ensure that the solution set is valid under the operations performed during the solving process.

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