Video Transcript
Find the value of 𝑥 if one-half 𝑥
minus three-quarters is equal to seven-eighths.
In this question, we are given an
equation and an unknown 𝑥 and asked to use this equation to determine its
value. To do this, we can start by
recalling that we can apply the same operations to both sides of the equation to
isolate 𝑥 on one side of the equation.
We can start by adding
three-quarters to both sides of the equation. On the left-hand side, we have
negative three-quarters plus three-quarters equals zero. So the left-hand side is one-half
𝑥. And on the right-hand side of the
equation, we have seven-eighths plus three-quarters.
At this point, there are two
options. We can either divide both sides of
the equation by one-half or simplify the right-hand side of the equation first. To add the fractions on the
right-hand side of the equation, they need to have the same denominator. We can multiply the numerator and
denominator of three-quarters by two to obtain six-eighths. We can now add the fractions
together by adding their numerators. We get one-half 𝑥 is equal to 13
over eight.
We can now isolate 𝑥 on the
left-hand side of the equation by dividing both sides of the equation by
one-half. We can then recall that dividing by
a fraction is the same as multiplying by its reciprocal. So we can instead multiply both
sides of the equation by two to get 𝑥 equals 13 over four.
We can verify that this is the
solution by substituting this value back into the equation. If we did this, we would see that
one-half of 13 over four minus three-quarters is equal to seven-eighths, verifying
that 𝑥 is equal to 13 over four.
