QuestionSolve for $n$ in the equation $3|2-5n|=0$ .

Studdy Solution

STEP 1

Assumptions1. The equation given is $3|-5n|=0$ . We need to find the value of $n$ that satisfies this equation

STEP 2

The absolute value of a number is its distance from zero on the number line, and is always non-negative. Therefore, if $|2-5n|=0$ , then $|2-5n|$ must be equal to zero.
$|2-5n|=0 \Rightarrow |2-5n|=0$

STEP 3

The only number whose absolute value is zero is zero itself. Therefore, the expression inside the absolute value, $2-5n$ , must be equal to zero.
$|2-5n|=0 \Rightarrow2-5n=0$

STEP 4

Now, we can solve the equation $2-n=0$ for $n$ . First, we isolate the term with $n$ on one side of the equation.
2-n=0 \Rightarrown=2

STEP 5

Finally, we divide both sides of the equation by5 to solve for $n$ .
$5n=2 \Rightarrow n=\frac{2}{5}$ So, the solution for $n$ in the equation $3|2-5n|=0$ is $n=\frac{2}{5}$ .

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