Math

QuestionSolve the equation 52(n+43)=3n32-\frac{5}{2}(n + \frac{4}{3}) = 3n - \frac{3}{2}.

Studdy Solution

STEP 1

Assumptions1. The equation to solve is 5/(n+4/3)=3n3/-5 /(n+4 /3)=3 n-3 / . We are solving for the variable nn

STEP 2

First, let's simplify the equation by multiplying both sides by2 to get rid of the fractions.
2(5/2(n+4/))=2(n/2)2(-5 /2(n+4 /)) =2(n - /2)

STEP 3

This simplifies to5(n+/3)=6n3-5(n+ /3) =6n -3

STEP 4

Next, distribute the - on the left side of the equationn20/3=6n3-n -20 /3 =6n -3

STEP 5

Multiply both sides by3 to get rid of the fraction3(5n20/3)=3(n3)3(-5n -20 /3) =3(n -3)

STEP 6

This simplifies to15n20=18n9-15n -20 =18n -9

STEP 7

Next, let's get all the nn terms on one side and the constants on the other. We can do this by adding 15n15n to both sides and adding9 to both sides15n+15n20+9=18n+15n9+9-15n +15n -20 +9 =18n +15n -9 +9

STEP 8

This simplifies to11=33n-11 =33n

STEP 9

Finally, divide both sides by33 to solve for nnn=11/33n = -11 /33

STEP 10

This simplifies ton=/3n = - /3So, the solution to the equation is n=/3n = - /3.

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