Answer:
Please check the explanation part for more details.
Step-by-step explanation:
1. Solve [tex]7y - 6= 2y + 8[/tex]
Send all components contain [tex]y[/tex] to the left, the other components to the right:
<=> [tex]7y - 6 = 2y + 8[/tex]
(sign of [tex]2y[/tex] is changed from negative to positive, sign of [tex]6[/tex] is changed from negative to positive)
<=> [tex]5y = 14[/tex]
Divide both sides of equation by [tex]5[/tex]:
<=> [tex]y = \frac{14}{5}[/tex]
2. Show that [tex]\frac{7}{8} - \frac{5}{6} =\frac{1}{24}[/tex]
First, we prove that [tex]24[/tex] is least common multiple(LCM) of the denominators of [tex]2[/tex] components on the left side ([tex]8[/tex] and [tex]6[/tex]).
[tex]8 = 2^{3}[/tex]
6 = [tex]2[/tex] x [tex]3[/tex]
=> LCM = [tex]2^{3}[/tex] x [tex]3[/tex] = [tex]8[/tex] x [tex]3[/tex] = [tex]24[/tex]
Multiply the first component [tex]\frac{7}{8}[/tex] by a factor which is equal to the quotient of LCM and denominator: [tex]\frac{24}{8} = 3[/tex]
=> [tex]\frac{7}{8} = \frac{7*3}{8*3} = \frac{21}{24}[/tex]
Multiply the second component [tex]\frac{5}{6}[/tex] by a factor which is equal to the quotient of LCM and denominator: [tex]\frac{24}{6} = 4[/tex]
=>[tex]\frac{5}{6} = \frac{5*4}{6*4} = \frac{20}{24}[/tex]
=>[tex]\frac{7}{8} -\frac{5}{6} = \frac{21}{24} - \frac{20}{24} = \frac{1}{24}[/tex]
3. Show that [tex]\frac{5}{8} / \frac{7}{12} = \frac{11}{14}[/tex]
[tex]\frac{5}{8} / \frac{7}{12} =[/tex] [tex]\frac{5}{8} * \frac{12}{7} =[/tex] [tex]\frac{60}{56} =\frac{60/4}{56/4} = \frac{15}{14} = 1\frac{1}{14}[/tex]
4. [tex]\frac{v4*v7}{vt} = \frac{v}{v} * \frac{v*4*7}{t} = \frac{v*28}{t}[/tex]
Hope this helps!
:)
