Select the correct alternative from the given choices. Find...

Select the correct alternative from the given choices.
Find the range of the real values of $x$ satisfying $8-3 x \leq 5$ and $4 x+5 \leq-7$.
(A) $[-3,1]$
(B) $(-\infty,-3] \cup[1, \infty)$
(C) $(-3,1)$
(D) $\phi$

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Key Concepts

Linear Inequalities

Linear inequalities involve a linear expression compared to another or a constant using inequality symbols like <, ?, >, or ?. They are similar to linear equations but instead of an equality, they establish a range of possible values that satisfy the condition.

Solving Linear Inequalities

The process of solving linear inequalities involves isolating the variable on one side of the inequality. This is done through operations such as addition, subtraction, multiplication, or division, with special care taken that multiplying or dividing by negative values reverses the direction of the inequality.

Compound Inequalities

Compound inequalities are statements that combine two or more inequalities using logical connectors such as 'and' or 'or'. They require determining the set of values that satisfy all the individual inequalities when combined, often leading to the intersection or union of solution sets.

Intersection of Solution Sets

The concept of the intersection of solution sets is crucial when dealing with compound inequalities connected by 'and'. It involves finding the common values that simultaneously satisfy all presented inequalities, ensuring that every condition in the problem is met.

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