Find the value of 𝑥 if 𝑥 plus one-half equals one-fifth.
In this question, we are given an equation involving an unknown 𝑥 and we are asked
to find the value of this unknown. To answer this question, we can start by recalling that in an equation, both sides of
the equation are equal. So, in this case, we have that 𝑥 plus one-half is equal to one-fifth. If we apply the same operations to both sides of the equation, they will remain
equal. This means we can try to isolate 𝑥 on one side of the equation to solve for 𝑥. To do this, we can start by subtracting one-half from both sides of the equation. This gives us 𝑥 plus one-half minus one-half is equal to one-fifth minus
one-half. We can then calculate that one-half minus one-half is equal to zero. This allows us to rewrite the equation as 𝑥 equals one-fifth minus one-half.
We can simplify the right-hand side of the equation by evaluating the
subtraction. To do this, the denominators of both fractions must be the same. The lowest common multiple of five and two is 10. So we rewrite both fractions to have a denominator of 10. We can rewrite one-fifth as two over 10 and one-half as five over 10. We can then evaluate the subtraction by subtracting the numerators. We obtain two minus five all over 10. We can calculate that this is equal to negative three over 10.
We can verify that this is a solution to the equation by substituting this value back
into the equation. If we did this, we would find that negative three-tenths plus one-half is equal to
one-fifth, verifying that the value of 𝑥 is negative three over 10.