If we simplify the given expression, we get [tex]\frac{5x+42}{12}[/tex].
Step-by-step explanation:
Step 1; First we need to multiply the integers with the fractions and make the entire expression consist of only fractions.
2 × [tex]\frac{1}{8}[/tex]x = [tex]\frac{x}{4}[/tex], [tex]\frac{3x}{4}[/tex] remains the same, [tex]\frac{1}{6}[/tex] remains unchanged, [tex]\frac{7x}{12}[/tex] remains the same but 5 × [tex]\frac{2}{3}[/tex] = [tex]\frac{10}{3}[/tex]. So the expression becomes
[tex]\frac{x}{4}[/tex] + [tex]\frac{3x}{4}[/tex] + [tex]\frac{1}{6}[/tex] - [tex]\frac{7x}{12}[/tex] + [tex]\frac{10}{3}[/tex].
Step 2; We calculate the LCM of the denominators and multiply the numerator with the number that must be multiplied with the denominator to equal the LCM. The LCM of 3, 4, 6 and 12 is 12. So the expression becomes
([tex]\frac{x}{4}[/tex] × [tex]\frac{3}{3}[/tex]) + ([tex]\frac{3x}{4}[/tex] × [tex]\frac{3}{3}[/tex]) + ([tex]\frac{1}{6}[/tex] × [tex]\frac{2}{2}[/tex]) - ([tex]\frac{7x}{12}[/tex] × [tex]\frac{1}{1}[/tex]) + ([tex]\frac{10}{3}[/tex] × [tex]\frac{4}{4}[/tex]) = [tex]\frac{3x+9x+2-7x+40}{12}[/tex] = [tex]\frac{5x+42}{12}[/tex].
