Graphing Basic Inequalities Worksheet

📆 Updated: 1 Jan 1970
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Are you a middle school or high school student who wants to improve their understanding of graphing basic inequalities? Look no further, as we have created a comprehensive worksheet that focuses on this very topic. This worksheet will guide you through the steps of graphing inequalities, helping you grasp the concepts and become more confident in your math skills. Whether you are struggling with this concept or simply want to reinforce your knowledge, this worksheet is designed to cater to your needs.



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What is a basic inequality?

A basic inequality is a statement that compares two expressions using symbols such as < (less than), > (greater than), ? (less than or equal to), or ? (greater than or equal to). It shows the relationship between the values of the two expressions, indicating that one is either smaller or larger than the other. For example, 3x + 2 < 10 or y ? 5 are examples of basic inequalities.

What are the common symbols used to represent inequalities?

Common symbols used to represent inequalities include "<" for less than, ">" for greater than, "?" for less than or equal to, "?" for greater than or equal to, and "?" for not equal to. These symbols are used in mathematical expressions to show the relationship between two quantities that are not equal.

How do you graph the inequality y < 2?

To graph the inequality y < 2 on a coordinate plane, you would draw a dashed horizontal line at y = 2 and shade the area below the line. This indicates that all the points below the line satisfy the inequality y < 2. Make sure to keep the line dashed because the inequality is strictly less than, not less than or equal to.

How do you graph the inequality x > -3?

To graph the inequality x > -3 on a number line, first plot an open circle at -3 to represent that x is not equal to -3. Then shade the region to the right of -3 towards positive infinity to represent all values of x that are greater than -3. This creates a half line pointing to the right on the number line.

How do you determine if a point is a solution to an inequality?

To determine if a point is a solution to an inequality, you substitute the coordinates of the point into the inequality and simplify to see if the statement is true or false. If the inequality holds true after substitution, then the point is a solution; if the inequality is false, then the point is not a solution to the inequality.

How do you shade the region on a graph representing the solution to an inequality?

To shade the region on a graph representing the solution to an inequality, first graph the boundary line (dashed if it's a strict inequality, solid if it's non-strict). Next, select a test point not on the boundary line and substitute its coordinates into the inequality to determine which side of the line is the solution region. Finally, shade the side of the boundary line that includes the test point to represent the solution to the inequality.

How do you graph the inequality 3x + 2y ? 6?

To graph the inequality 3x + 2y ? 6, first rewrite it in slope-intercept form by isolating y: y ? -3/2x + 3. Next, start by graphing the line y = -3/2x + 3 as a solid line (since it's inclusive of the line itself). Then, since we want y values greater than or equal to -3/2x + 3 (meaning above the line), shade the area above the line to represent the solution set of the inequality.

How do you graph the inequality 5x - y < 10?

To graph the inequality 5x - y < 10, you first need to rewrite it in slope-intercept form (y = mx + b). Start by isolating y: y > 5x - 10. Then, graph the line y = 5x - 10 as a dashed line (since it is a strict inequality). Finally, shade the region below the line to show where the y values are less than 5x - 10.

What is the difference between an open circle and a closed circle on a graph representing an inequality?

In a graph representing an inequality, an open circle is used to indicate that the endpoint is not included in the solution set, while a closed circle is used to indicate that the endpoint is included in the solution set. The open circle is typically used for strict inequalities (<, >) where the values are not equal to the endpoint, while the closed circle is used for non-strict inequalities (?, ?) where the values are equal to the endpoint.

How do you write the solution to an inequality in interval notation?

To write the solution to an inequality in interval notation, you need to first find the values of the variable that satisfy the inequality. Then, use parentheses or brackets to represent whether the endpoint values are included or excluded in the solution set. For example, if the solution set is all real numbers greater than 3 (3 excluded), it would be written as (3, ?) in interval notation. Remember that round brackets '(' mean the endpoint is excluded, while square brackets '[' mean the endpoint is included in the interval.

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