Solve each inequality. Graph the solution. 3(4 x-1) ≥2(4-x)...

Name: Problem 77, Chapter 1: Algebra 2
Uploaded: 2020-03-20T22:31:38-08:00
Duration: 2 min 17 s
Channel: Kelsey Van Horn
Description: Solve each inequality. Graph the solution. 3(4 x-1) ≥2(4-x)

Key Concepts

Combining Like Terms and Isolating the Variable

After using the distributive property, the next step in solving inequalities is to combine like terms and isolate the variable. This involves moving terms from one side of the inequality to the other by adding or subtracting and then dividing or multiplying to solve for the variable while preserving the inequality sign (and reversing it if multiplying or dividing by a negative number).

Linear Inequality

A linear inequality is an inequality that involves a linear expression in one variable. It is similar to a linear equation but uses inequality signs (such as <, ?, >, or ?) instead of an equals sign. Solving a linear inequality involves finding all values of the variable that make the inequality true.

Distributive Property

The distributive property is a key algebraic rule that is used to expand expressions that have a factor multiplying a sum or difference. It is applied by multiplying the factor outside the parentheses by each term inside, which is essential for simplifying and solving algebraic expressions, including inequalities.

Graphing on a Number Line

Graphing the solution of an inequality on a number line is a visual representation of the set of all values that satisfy the inequality. It typically involves marking a point on the number line (using an open circle if the endpoint is not included or a closed circle if it is) and shading the region that corresponds to the solution set.

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