Select the correct alternative from the given choices. If 5...

Select the correct alternative from the given choices.
If $5 x-8<2 x+9$ and $4 x+7>7 x-8$, then the range of the values of $x$ that satisfies the inequalities is
(A) $(5, \infty)$
(B) $(-\infty, 5)$
(C) $\left(5, \frac{17}{3}\right)$
(D) $\left(-\infty, \frac{17}{3}\right)$

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Key Concepts

Interval Notation

Interval notation is a concise way to represent the set of solutions to an inequality. It uses brackets and parentheses to denote whether endpoints are included or excluded, thereby providing a clear and standard format for expressing numerical ranges.

Intersection of Solutions

After solving individual inequalities in a compound inequality, the overall solution is found by taking the intersection of the individual solution sets. This means identifying the values that simultaneously satisfy all the inequalities involved.

Compound Inequalities

Compound inequalities are sets of inequalities that need to be satisfied simultaneously. They usually involve finding the set of values that meet all given conditions and often require solving each inequality separately before determining their common solution.

Linear Inequalities

This concept involves working with inequalities that include a variable and a constant, where one side of the inequality is compared to the other using signs like <, >, ?, or ?. It requires careful manipulation similar to solving linear equations while keeping in mind the rules associated with reversing the inequality sign when multiplying or dividing by a negative number.

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