Question $5=\frac{5(4 n-1)}{3}$

Studdy Solution

STEP 1

1. The equation given is $5 = \frac{5(4n-1)}{3}$ .
2. We are solving for the variable $n$ .
3. The equation involves a fraction, which suggests that we may need to eliminate the fraction to solve for $n$ .

STEP 2

1. Eliminate the fraction by multiplying both sides by the denominator.
2. Simplify the resulting equation.
3. Solve for $n$ .

STEP 3

To eliminate the fraction, multiply both sides of the equation by the denominator, which is 3:
$3 \cdot 5 = 3 \cdot \frac{5(4n-1)}{3}$
This simplifies to:
$15 = 5(4n-1)$

STEP 4

Distribute the 5 on the right-hand side of the equation:
$15 = 5 \cdot 4n - 5 \cdot 1$
This simplifies to:
$15 = 20n - 5$

STEP 5

To solve for $n$ , first add 5 to both sides to isolate the term with $n$ :
$15 + 5 = 20n - 5 + 5$
This simplifies to:
$20 = 20n$
Next, divide both sides by 20 to solve for $n$ :
$\frac{20}{20} = \frac{20n}{20}$
This simplifies to:
$1 = n$
The solution is $n = \boxed{1}$ .

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