Solve each inequality and graph the solution. m-(3 m-2)+6<7...

Key Concepts

Linear Inequalities

Linear inequalities are mathematical expressions that compare two values or expressions using inequality signs (such as <, >, ?, or ?) instead of an equality sign. They involve variables to the first power and require similar solution methods as linear equations, with the added step of ensuring that inequality direction is preserved or correctly reversed when multiplying or dividing both sides by a negative number.

Algebraic Simplification

Algebraic simplification in the context of inequalities involves combining like terms, applying the distributive property, and rearranging the equation to isolate the variable. This step-by-step process reduces the expression to a simpler form that makes the inequality easier to solve.

Properties of Inequalities

The properties of inequalities are rules that govern how inequalities can be manipulated. This includes adding or subtracting the same value on both sides without altering the inequality, and multiplying or dividing both sides by a positive number while maintaining the inequality’s direction. It also emphasizes the need to reverse the inequality sign when multiplying or dividing by a negative number.

Graphing on the Number Line

Once the solution to an inequality is found, graphing involves representing the set of possible values visually on a number line. This typically includes marking a point that represents the boundary and shading the region that satisfies the inequality, using an open circle for strict inequalities and a closed circle for inclusive ones.

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