In all exercises other than ∅, use interval notation to express solution sets and graph each sol

step 1 All righty, 36. I have 8x plus 3 is greater than 3 times of quantity 2x plus 1 plus x plus 5. No

In all exercises other than ∅, use interval notation to...

In all exercises other than $\varnothing$, use interval notation to express solution sets and graph each solution set on a number line. In Exercises $27-50,$ solve each linear inequality.
$$
8 x+3>3(2 x+1)+x+5
$$

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Key Concepts

Linear Inequalities

Linear inequalities are mathematical expressions involving linear functions that use inequality symbols (such as >, <, ?, and ?) instead of an equals sign. They are solved by applying similar techniques as used in solving linear equations, such as combining like terms and isolating the variable, while also taking care to reverse the inequality sign when multiplying or dividing by a negative number.

Interval Notation

Interval notation is a succinct method of expressing sets of numbers, especially solution sets of inequalities. It uses brackets to denote inclusion of endpoints and parentheses to denote exclusion, thereby providing a clear and concise description of all the numbers that satisfy the inequality.

Graphing on a Number Line

Graphing on a number line is a visual tool used to represent solution sets of inequalities. It involves marking the identified solution interval on a horizontal line and using open circles for endpoints that are not included in the solution, or closed circles for those that are included, making it easier to visualize the range of valid solutions.

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