Question

If (p+1)-(2p+4)/3-5p = 1/23, find p

Answer 1

Answer:

The value of p is - 4.

Step-by-step-explanation:

The given equation is

$\displaystyle{\sf\:\dfrac{(\:p\:+\:1\:)\:-\:(\:2p\:+\:4\:)}{3\:-\:5p}\:=\:\dfrac{1}{23}}$

We have to find the value of p.

Now,

$\displaystyle{\sf\:\dfrac{(\:p\:+\:1\:)\:-\:(\:2p\:+\:4\:)}{3\:-\:5p}\:=\:\dfrac{1}{23}}$

$\displaystyle{\implies\sf\:\dfrac{p\:+\:1\:-\:2p\:-\:4}{3\:-\:5p}\:=\:\dfrac{1}{23}}$

$\displaystyle{\implies\sf\:23\:(\:p\:-\:2p\:+\:1\:-\:4\:)\:=\:3\:-\:5p}$

$\displaystyle{\implies\sf\:23\:(\:-\:p\:-\:3\:)\:=\:3\:-\:5p}$

$\displaystyle{\implies\sf\:-\:23p\:-\:69\:=\:3\:-\:5p}$

$\displaystyle{\implies\sf\:-\:23p\:+\:5p\:=\:3\:+\:69}$

$\displaystyle{\implies\sf\:-\:18p\:=\:72}$

$\displaystyle{\implies\sf\:p\:=\:-\:\cancel{\dfrac{72}{18}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:p\:=\:-\:4\:}}}}$

∴ The value of p is - 4.

Answer 2

Answer:

• The value of p is -4.

Step-by-step explanation:

Given,

• $\tt \frac{(p + 1) - (2p + 4)}{3 - 5p} = \frac{1}{23}$

To Find,

• The value of p.

Solution,

$:\implies \tt \frac{(p + 1) - (2p + 4)}{3 - 5p} = \frac{1}{23} \\ \\ :\implies \tt \frac{p + 1 - 2p - 4}{3 - 5p} = \frac{1}{23} \\ \\ :\implies \tt \frac{ - 3 - p}{3 - 5p} = \frac{1}{23} \\ \\ :\implies \tt 23( - 3 - p) = 3 - 5p\\ \\ :\implies \tt - 69 - 23p = 3 - 5p \\ \\ :\implies \tt - 69 - 3 = 23p - 5p \\ \\ :\implies \tt - 72 = 18p \\ \\ :\implies \color{red} \boxed{p = - 4}$

Verification,

$:\implies \tt \frac{(p + 1) - (2p + 4)}{3 - 5p} = \frac{1}{23} \\ \\ :\implies \tt \frac{( - 4 + 1) - (2( - 4) + 4)}{3 - 5( - 4)} = \frac{1}{23} \\ \\ :\implies \tt \frac{ - 4 + 1 - ( - 8 + 4)}{3 + 20} = \frac{1}{23} \\ \\ :\implies \tt \frac{ - 3 +8 - 4 }{23} = \frac{1}{23} \\ \\ :\implies \tt \frac{1}{23} = \frac{1}{23} \\ \\ :\implies \tt LHS = RHS$

Required Answer,

• The value of p is -4.