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Difficulty: EasySolving One-Variable Inequalities

Multiplying both sides of the inequality −x3<5-\frac{x}{3} < 5 by −3-3 results in the equivalent inequality x>−15x > -15.

Answer: Answer

Answer

True
The statement correctly applies the algebraic rule that multiplying an inequality by a negative number reverses the direction of the inequality sign, properly yielding x>−15x > -15.

Step-by-Step Solution

1
Identify the operation needed to isolate the variable xx.
Multiply both sides of the inequality −x3<5-\frac{x}{3} < 5 by −3-3.
The variable xx is being divided by −3-3, so multiplying by −3-3 is the inverse operation.
2
Perform the multiplication and apply the inequality division/multiplication rule.
−3×(−x3)>−3×5-3 \times (-\frac{x}{3}) > -3 \times 5, which simplifies to x>−15x > -15.
When multiplying or dividing an inequality by a negative number, the inequality symbol must be reversed to maintain a true mathematical statement.

Key Concept

When solving inequalities, multiplying or dividing both sides by a negative number requires flipping the inequality sign.
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Topics

Solving One-Variable Inequalities

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