Solve each linear inequality. Other than ∅, graph the solution set on a number line. 4(3 x-2)-3

step 1 For problem 21, we're given an inequality here that we need to solve. So there's a lot to unpack

Solve each linear inequality. Other than ∅, graph the...

Key Concepts

Linear Inequalities

Linear inequalities are mathematical expressions that use inequality symbols (such as <, >, ?, or ?) to show the relationship between two linear expressions. They are solved in ways similar to linear equations, but the solution sets are typically ranges of values rather than single numbers.

Distributive Property

The distributive property is an algebraic rule used to multiply a single term by each term within a parenthesis. It is often the first step in solving equations and inequalities as it helps to eliminate parentheses and simplify the expression.

Combining Like Terms

Combining like terms involves simplifying algebraic expressions by adding or subtracting terms that have the same variables raised to the same powers. This is a crucial step in reducing the inequality to a simpler form that can be solved easily.

Isolating the Variable

Isolating the variable means rearranging an inequality so that the variable appears on one side and all constant terms on the other, allowing for the determination of the variable’s range of values. Care must be taken during this process, especially when multiplying or dividing by a negative number, as it reverses the inequality sign.

Graphing on a Number Line

Graphing the solution set on a number line provides a visual representation of all the possible solutions of an inequality. It involves marking the boundary points and shading the region that represents the range of values that satisfy the inequality.

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