Solve each inequality. Write the solution set in interval notation and graph it. -4(3 y+2) ≤28

Name: Problem 93, Chapter 5: Elementary and Intermediate Algebra
Uploaded: 2020-03-24T02:54:31-08:00
Duration: 1 min 32 s
Channel: Heather Zimmers
Description: Solve each inequality. Write the solution set in interval notation and graph it. -4(3 y+2) ≤28

step 1 Here's a review problem, solving and graphing an inequality. So I'm going to start by dividing b

Solve each inequality. Write the solution set in interval...

Key Concepts

Interval Notation

Interval notation is a concise way of representing the solution set of an inequality. It shows the lower and upper bounds of the solution set with parentheses or brackets, where brackets indicate that an endpoint is included and parentheses indicate that it is not.

Multiplication or Division by a Negative Number

When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality sign must be reversed. This rule is critical in ensuring the solution set accurately reflects the original inequality's constraints.

Graphing on a Number Line

Graphing the solution to an inequality on a number line provides a visual representation of all the values that satisfy the inequality. It involves marking the endpoints of the interval (using open or closed circles depending on whether the endpoints are included) and shading the region that represents the solution set.

Distributive Property

The distributive property allows you to multiply a factor across terms inside parentheses. In the context of solving any equation or inequality, this property is used to eliminate parentheses and simplify the expression, making subsequent steps like isolating the variable more straightforward.

Solving Linear Inequalities

This concept involves isolating the variable on one side of the inequality by performing algebraic operations such as addition, subtraction, multiplication, or division. The process is similar to solving a linear equation, but special care must be taken, especially when dealing with the direction of the inequality sign.

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