Find all possible values of 𝑥 given the modulus of 𝑥 plus a half is equal to three-quarters.
We know that the modulus or absolute value of a number is its distance from zero. This means that we have two possible solutions: either 𝑥 plus a half is equal to three-quarters or 𝑥 plus a half is equal to negative three-quarters. In both of these equations, we need to subtract one-half from both sides. As subtracting one-half is the same as subtracting two-quarters, we have values of 𝑥 equal to one-quarter and negative five-quarters.
The two values that satisfy the equation the absolute value or modulus of 𝑥 plus one-half is equal to three-quarters are one-quarter and negative five-quarters.