Understanding Absolute Value Equations with No Solution

In this video, Mr. J explains absolute value equations that have no solution. He emphasizes that absolute value represents distance from zero and cannot be negative. Through three examples, he demonstrates why equations like x = -5, w + 7 = -11, and -2 * (3a - 14) = 16 have no solutions. The key takeaway is that if an absolute value equals a negative number, the equation has no solution.

What is the absolute value of a number?

• The negative of the number

• The number itself

• The square of the number

• The distance from zero

Why can't the absolute value of a number be negative?

• Because it is always positive or zero

• Because it is always zero

• Because it is always negative

• Because it is always a whole number

In the equation |x| = -5, why is there no solution?

• Because x is always zero

• Because absolute value cannot be negative

• Because x is always positive

• Because x is not defined

What is the absolute value of -5?

• 10

• 0

• 5

• -5

In the equation |w + 7| = -11, why is there no solution?

• Because w is always positive

• Because absolute value cannot be negative

• Because w is always zero

• Because w is not defined

What is the first step in solving -2 * |3a - 14| = 16?

• Add 2 to both sides

• Multiply both sides by 2

• Subtract 16 from both sides

• Divide both sides by -2

After isolating the absolute value in -2 * |3a - 14| = 16, what does the equation become?

• |3a - 14| = 8

• |3a - 14| = -8

• |3a - 14| = 16

• |3a - 14| = -16

Why does the equation |3a - 14| = -8 have no solution?

• Because absolute value cannot be negative

• Because 3a is not defined

• Because 3a is always zero

• Because 3a is always positive

What should you remember about absolute value equations equaling a negative?

• They always have one solution

• They always have two solutions

• They have infinite solutions

• They have no solution

What is the key takeaway from the video?

• Absolute values are always positive or zero

• Absolute values are always negative

• Absolute values are always zero

• Absolute values can be negative