Mathematics

Mathematics

Problem

Solve 3(2x−5)−6x+4≥43(2x-5)-6x+4 \ge 4. Which of the following describes the solution set? a) x≥54x\ge \dfrac{5}{4} b) No real solution c) All real numbers d) x>0x>0
Intuitive explanation

This is a linear inequality—you're finding all values of xx that make the statement true. The key is to simplify the left side by distributing and combining like terms, then isolate xx using the same moves you'd use for equations. Remember: the inequality sign stays the same when you add, subtract, multiply, or divide by positive numbers, but flips if you multiply or divide by a negative.

Intuitive explanation

This is a linear inequality—you're finding all values of xx that make the statement true. The key is to simplify the left side by distributing and combining like terms, then isolate xx using the same moves you'd use for equations. Remember: the inequality sign stays the same when you add, subtract, multiply, or divide by positive numbers, but flips if you multiply or divide by a negative.

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