Solve:
[tex]\frac{1}{4}p-\frac{2}{5}=\frac{3}{4}p+7[/tex]The LCM of the denominators is 4*5 = 20. So we multiply each term by 20 to eliminate denominators:
[tex]20\cdot\frac{1}{4}p-20\cdot\frac{2}{5}=20\cdot\frac{3}{4}p+20\cdot7[/tex]Operating:
[tex]5p-8=15p+140[/tex]Adding 8 and subtracting 15p:
[tex]5p-15p=8+140[/tex]Simplifying:
[tex]-10p=148[/tex]Dividing by -10:
[tex]p=\frac{148}{-10}[/tex]Simplifying:
[tex]p=-\frac{74}{5}[/tex]