Video Transcript
Find the value of 𝑥 for which the
rational number 𝑥 minus 18 over 26 does not have a multiplicative inverse.
We need to think about what we know
about a value that does not have a multiplicative inverse. We know that all numbers except
zero have a reciprocal. And that multiplicative inverse is
another word for reciprocal. And so we can say that when 𝑥
minus 18 over 26 equals zero, it does not have a reciprocal. We now need to find a value of 𝑥
that makes 𝑥 minus 18 over 26 equal to zero. We can get the 26 out of the
denominator by multiplying both sides of the equation by 26. 26 times zero equals zero. And 𝑥 minus 18 equals zero.
To find 𝑥, we need to add 18 to
both sides. Zero plus 18 equals 18. And 𝑥 minus 18 plus 18 just equals
𝑥. We can flip that around to say 𝑥
equals 18. We’re saying that 18 minus 18 over
26 does not have a reciprocal because 18 minus 18 equals zero. And zero over 26 equals zero. Since zero does not have a
multiplicative inverse, we can say that when 𝑥 is 18, this expression does not have
a multiplicative inverse.
