Solve the inequality and specify the answer using interval notation. (x-1)/(4)-(2 x+3)/(5) ≤x

Name: Problem 6, Chapter 2: Precalculus
Uploaded: 2020-07-14T20:05:42-08:00
Duration: 2 min 23 s
Channel: Jonathon Brumley
Description: Solve the inequality and specify the answer using interval notation. (x-1)/(4)-(2 x+3)/(5) ≤x

step 1 We have an inequality that is starting with three of the same variable. To solve this, we're fir

Solve the inequality and specify the answer using interval...

Key Concepts

Linear Inequalities

This concept involves expressions that contain an inequality instead of an equality, typically using symbols like <, ?, >, or ?. The goal is to isolate the variable on one side of the inequality to determine the range of values that satisfy the condition. Techniques for solving linear inequalities are fundamental in algebra and often resemble those used in solving linear equations, with additional attention to the direction of the inequality when multiplying or dividing by negative numbers.

Clearing Fractions

In inequalities or equations involving fractions, one common method is to multiply both sides by the least common denominator (LCD) to eliminate fractions. This step simplifies the inequality to a form where standard algebraic techniques, such as combining like terms and isolating the variable, can be applied more easily. This approach is crucial for reducing potential errors and streamlining the solution process.

Combining Like Terms and Rearrangement

After clearing fractions, it is necessary to simplify the inequality by combining like terms and rearranging the expression so the variable terms are on one side and the constant terms on the other. This manipulation allows for a straightforward solution where the variable can be isolated, which is a key strategy in solving any linear inequality.

Interval Notation

Interval notation is a compact and standardized way of representing the solution set of an inequality on the real number line. It uses parentheses and brackets to indicate open and closed intervals respectively. Understanding interval notation is essential for accurately conveying the range of values that satisfy an inequality and is widely used in algebra and higher-level mathematics.

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