Solve the Equation: -|3y²| with Negative Absolute Value

Absolute Value Properties with Negative Coefficients

−∣3y2∣= -\left|3y^2\right|=

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Step-by-step written solution

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1

Understand the problem

−∣3y2∣= -\left|3y^2\right|=

2

Step-by-step solution

The absolute value of 3y2 3y^2 is 3y2 3y^2 itself because 3y2 3y^2 is always non-negative regardless of the value of y y since any real number squared is non-negative. The negative sign outside the absolute value indicates that the expression−∣3y2∣ -\left|3y^2\right| evaluates to −3y2 -3y^2 .

3

Final Answer

−3y2 -3y^2

Key Points to Remember

Essential concepts to master this topic
  • Property: Absolute value of any squared expression is positive
  • Technique: Since 3y2≥0 3y^2 \geq 0 , then ∣3y2∣=3y2 |3y^2| = 3y^2
  • Check: Test with y = 2: −∣3(4)∣=−12=−3(4) -|3(4)| = -12 = -3(4) ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring the negative sign outside absolute value bars
    Don't think −∣3y2∣=3y2 -|3y^2| = 3y^2 by removing the negative sign! This gives a positive result when the answer should be negative or zero. Always apply the negative sign after evaluating the absolute value.

Practice Quiz

Test your knowledge with interactive questions

Determine the absolute value of the following number:

\( \left|18\right|= \)

FAQ

Everything you need to know about this question

Why is the absolute value of 3y2 3y^2 just 3y2 3y^2 ?

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Because 3y2 3y^2 is always non-negative! When you square any real number, you get a positive result (or zero). Since 3 is positive, 3y2≥0 3y^2 \geq 0 for all values of y.

What does the negative sign outside the absolute value do?

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The negative sign flips the sign of whatever comes out of the absolute value. Since ∣3y2∣=3y2 |3y^2| = 3y^2 , then −∣3y2∣=−3y2 -|3y^2| = -3y^2 .

Is −3y2 -3y^2 always negative?

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Almost always! It's negative when y ≠ 0, and equals zero when y = 0. Since y2≥0 y^2 \geq 0 , we have −3y2≤0 -3y^2 \leq 0 .

How can I verify this with specific numbers?

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Try y = 2: −∣3(2)2∣=−∣12∣=−12 -|3(2)^2| = -|12| = -12
And −3(2)2=−3(4)=−12 -3(2)^2 = -3(4) = -12 ✓
Both methods give the same answer!

What if y is negative, like y = -2?

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It doesn't matter! (−2)2=4 (-2)^2 = 4 , so:
−∣3(−2)2∣=−∣3(4)∣=−∣12∣=−12 -|3(-2)^2| = -|3(4)| = -|12| = -12
The result is the same because squaring removes the negative sign.

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