How do you solve #\frac { 14p } { 5} - 3= \frac { 3p } { 8} + \frac { 7} { 30}#?

Answer 1

#p=4/3#

If an equation has fractions, you can get rid of them immediately by multiplying each term by the LCM of the denominators. (The LCD) so that you can cancel the denominators

In this case it is #120#
#(color(blue)(120xx) 14p)/5 - color(blue)(120xx) 3= (color(blue)(120xx)3p)/8 + (color(blue)(120xx)7)/30#
#(color(blue)(cancel(120)^24xx) 14p)/cancel5 - color(blue)(120)xx 3= (color(blue)(cancel(120)^15xx)3p)/cancel8 + (color(blue)(cancel(120)^4xx)7)/cancel30#
#336p -360 = 45p +28#
#336p-45p = 28+360#
#291p = 388#
#p = 388/291#
#p=4/3#
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Answer 2

#p=1\frac{1}{3}#

#\frac{14p}{5}-3=\frac{3p}{8}+\frac{7}{30}#

Rearrange the terms so the terms with variables are on one side, and the constants are on the other side:

#\frac{14p}{5}-\frac{3p}{8}=\frac{3}{70}+3#
Find a common denominator on the LHS, which is #40#:
#\frac{14p\cdot color(red)(8)}{5\cdot color(red)(8)}-\frac{3p\cdot color(green)(5)}{8\cdot color(green)(5)}=\frac{7}{30}+3#
#\rightarrow\frac{122p}{40}-\frac{15p}{40}=\frac{7}{30}+3#
Change the #3# on the RHS to have a denominator of #30#:
#\frac{112p}{40}-\frac{15p}{40}=\frac{7}{30}+\frac{90}{30}#

Simplify both sides:

#\frac{color(magenta)(97p)}{color(blue)(40)}=\frac{color(blue)(97)}{color(magenta)(30)}#

Cross multiply:

#color(magenta)(97p)\cdot color(magenta)(30)=color(blue)(40)\cdot color(blue)(97)#

Evaluate both sides:

#3880=2910p#
Isolate for #p#:
#p=1\frac{1}{3}#
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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