Use the x -intercept method to solve the inequality. Write the solution set in set-builder or in

Use the x -intercept method to solve the inequality. Write...

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Key Concepts

Linear Inequalities

Linear inequalities involve expressions of the first degree and require determining the set of all variable values that make the inequality true. They are solved by performing algebraic operations similar to those used with linear equations while keeping in mind that multiplying or dividing by a negative number reverses the inequality sign.

x-intercept Method

The x-intercept method is a graphical approach where the solution to an inequality is determined by finding where the graph of the function crosses the x-axis. This method helps to visually identify the points where the expression changes sign, which are critical in solving inequalities and establishing the intervals that satisfy the inequality.

Interval and Set-Builder Notation

Interval notation and set-builder notation are standardized ways to represent the solution sets of inequalities. Interval notation expresses the solutions as a range between endpoints, using brackets to denote inclusivity or parentheses for exclusivity, while set-builder notation describes the set by stating the properties that its elements satisfy.

Transcript

00:01 Okay, so i'm given this inequality and i want to solve it using the x interset method.

00:04 What is the x interset method? well, what it's saying is i have two sides of my inequality on my left side and my right side.

00:13 What i can do is i can move my entire right side to my left side, right? but just subtracting the entire left side from both sides and call this an equation.

00:25 So i can have an equation, y equals x minus 2 minus 1 3rd x.

00:29 And i have the equation of a line right here.

00:33 Now, in this equation, i care specifically about my x intercept.

00:37 What is my x intercept? that is where i cross the x axis, right? the left to right axis.

00:44 And i cross it at the point three, zero.

00:47 But i care specifically when this entire value, right, x minus 2 minus 1 3rdx, is going to be less than or equal to zero.

00:57 What does it mean if it's less than or equal to zero? well, it's below the x -axis, right? it's where the ys are all negative along this line here.

01:06 All the ys are negative.

01:08 And this is going to happen from my x -intercept method.

01:10 Starts at 3.

01:11 I can hit 3, right? all the x values such that x is less than 3 and can also be equal to 3 since i can include my x -intercept because it can be less than or equal to 0.

01:23 Okay, that's my solution in set builder notation...

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