Solve each inequality. Graph the solution set and write it using interval notation. (x-7)/(2)-(x

step 1 To solve this problem, the first thing I want to do is get rid of the fractions. And so to do th

Solve each inequality. Graph the solution set and write it...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Graphing on a Number Line

Graphing on a number line is a visual way to represent the solution set of an inequality. It involves drawing a line, marking key points, and using open circles for values not included and closed circles for values that are included, along with a shaded region that represents all the numbers satisfying the inequality.

Interval Notation

Interval notation is a system to represent sets of numbers along the number line. It uses brackets to indicate whether endpoints are included (using [ or ]) or excluded (using ( or )), and simplifies the description of continuous ranges of values that satisfy an inequality.

Clearing Fractions

Clearing fractions is a technique used to simplify equations or inequalities that contain fractional expressions. This is done by finding the least common denominator (LCD) of all fractions involved and multiplying each term by it, thereby eliminating the fractions and making the expression easier to manipulate.

Linear Inequalities

Linear inequalities involve expressions where a linear expression is related to another expression using inequality symbols such as <, >, ?, or ?. Solving them follows similar steps to solving linear equations, but extra care must be taken, especially when multiplying or dividing by negative numbers, as this reverses the inequality sign.

Transcript

Please give Ace some feedback