Sure, let's go step-by-step to solve the given expression and find the numerator.
We start with the expression:
[tex]\[ 5x - \frac{3}{4}x \][/tex]
First, we need to combine like terms. The terms [tex]\(5x\)[/tex] and [tex]\(\frac{3}{4}x\)[/tex] are like terms because they both have the variable [tex]\(x\)[/tex]. To combine these, we need a common denominator for their coefficients.
1. We convert the whole number coefficient of [tex]\(5x\)[/tex] to a fraction with the same denominator as [tex]\(\frac{3}{4}x\)[/tex]. The common denominator is 4.
[tex]\[ 5x = \frac{20}{4}x \][/tex]
2. Now, we can subtract [tex]\(\frac{3}{4}x\)[/tex] from [tex]\(\frac{20}{4}x\)[/tex]:
[tex]\[ \frac{20}{4}x - \frac{3}{4}x \][/tex]
3. Subtract the numerators and keep the common denominator:
[tex]\[ \frac{20 - 3}{4}x = \frac{17}{4}x \][/tex]
4. The resulting fraction is [tex]\(\frac{17}{4}\)[/tex].
The numerator of this combined term is [tex]\(17\)[/tex].
