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Solve the following equation and then check your solution. Show all of your work.

-17+ n/5=33

3 answers

To solve the equation \(-17 + \frac{n}{5} = 33\), we can follow these steps:

  1. Isolate the term with \(n\): Start by adding 17 to both sides of the equation to eliminate \(-17\):

    \[ -17 + \frac{n}{5} + 17 = 33 + 17 \]

    This simplifies to:

    \[ \frac{n}{5} = 50 \]

  2. Eliminate the fraction: To get rid of the fraction, multiply both sides of the equation by 5:

    \[ 5 \cdot \frac{n}{5} = 5 \cdot 50 \]

    This simplifies to:

    \[ n = 250 \]

Now we have \(n = 250\).

  1. Check the solution: Substitute \(n = 250\) back into the original equation to verify:

    \[ -17 + \frac{250}{5} = 33 \]

    Calculate \(\frac{250}{5}\):

    \[ \frac{250}{5} = 50 \]

    Now substitute:

    \[ -17 + 50 = 33 \]

    Calculate the left side:

    \[ 33 = 33 \]

Since both sides of the equation are equal, the solution is confirmed.

Therefore, the solution to the equation \(-17 + \frac{n}{5} = 33\) is

\[ \boxed{250} \]

can you make it less advanced

Sure! Let’s solve the equation \(-17 + \frac{n}{5} = 33\) step by step in a simpler way.

Step 1: Get rid of \(-17\)

To make it easier, we can add 17 to both sides of the equation. This helps us move the \(-17\) away from the left side.

So we do:

\[ -17 + \frac{n}{5} + 17 = 33 + 17 \]

This simplifies to:

\[ \frac{n}{5} = 50 \]

Step 2: Get rid of the fraction

Now we have \(\frac{n}{5} = 50\). Next, we want to get \(n\) by itself. To do this, we can multiply both sides by 5 (because the \(\frac{1}{5}\) means we are dividing by 5).

So we multiply:

\[ 5 \cdot \frac{n}{5} = 5 \cdot 50 \]

This simplifies to:

\[ n = 250 \]

Step 3: Check the solution

Now we need to check if our solution \(n = 250\) is correct. We do this by putting \(n\) back into the original equation:

\[ -17 + \frac{250}{5} = 33 \]

Now let's calculate \(\frac{250}{5}\):

\[ \frac{250}{5} = 50 \]

Now we substitute that back into our equation:

\[ -17 + 50 = 33 \]

Now let's calculate the left side:

If we do \(-17 + 50\), we get:

\[ 33 = 33 \]

Since both sides are equal, it confirms that our solution is correct!

So, the final answer is:

\[ \boxed{250} \]