Video Transcript
Find the solution set of the
equation negative four 𝑥 plus three equals four.
We’re given the equation negative
four 𝑥 plus three equals four. This negative four 𝑥 means
negative four times 𝑥. And whatever that value is, we’re
adding three to it. We find the 𝑥-value by isolating
the 𝑥, by getting it by itself on one side of the equation. In order to get 𝑥 by itself, we
first subtract three from both sides. Negative four 𝑥 plus three minus
three equals negative four 𝑥. And four minus three equals
one.
Because we now have negative four
times 𝑥 equals one, to find 𝑥 by itself, we need to divide both sides of the
equation by negative four, which you might write like this or in the fraction form
like this. Negative four 𝑥 divided by
negative four equals 𝑥. And we need to be careful on the
right side because we have one divided by negative four. We can write that as a fraction,
negative one-fourth, or in the decimal format, negative 0.25.
Once we found negative one-fourth
for 𝑥, it’s worth plugging it back in to check. Negative four times negative
one-fourth equals one. And one plus three does equal four,
which means we found a correct value for 𝑥. But we should be careful here
because the question is asking for a solution set. And that means we’ll use the curly
brackets. There’s only one value in the
solution set. And that’s negative one-fourth,
which in set notation looks like this.
