For each Inequality, decide whether the solution is represented by x 4.5 a. -24>-6(x-0.

step 1 In problem four, it says, or it wants us to decide for each of these inequalities if the solutio

For each Inequality, decide whether the solution is...

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Key Concepts

Multiplication or Division by Negative Numbers

A key principle in working with inequalities is that when both sides of an inequality are multiplied or divided by a negative number, the direction of the inequality must be reversed. This is essential to correctly isolate the variable and determine the accurate solution interval.

Linear Inequalities

A linear inequality is similar to a linear equation, but instead of an equals sign, it uses inequality symbols (such as <, >, ?, or ?) to express a range of values that satisfy the condition. This concept is important for understanding how solutions can represent intervals on a number line.

Properties of Inequalities

When solving linear inequalities, arithmetic operations such as addition and subtraction are performed much like in equations, but special attention is needed when multiplying or dividing by negative numbers. These properties ensure that the validity of the inequality is maintained or adjusted appropriately during manipulations.

Distributive Property

The distributive property allows for the removal of parentheses by multiplying a factor by each term inside the parentheses. This step is often necessary to simplify the inequality and combine like terms, making it easier to solve for the variable.

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