Question57. $-5>p-\frac{1}{5}$

Studdy Solution

STEP 1

What is this asking? We need to find all the values of $p$ that make the inequality $-5 > p - \frac{1}{5}$ true. Watch out! Remember that when we multiply or divide both sides of an inequality by a negative number, we must flip the inequality sign!
But we won't need to do that here.

STEP 2

1. Isolate $p$
2. Express the solution

STEP 3

To get $p$ by itself, we need to add $\frac{1}{5}$ to both sides of the inequality.
Why both sides?
Because it's like a seesaw – to keep it balanced, whatever we do to one side, we gotta do to the other! $-5 + \frac{1}{5} > p - \frac{1}{5} + \frac{1}{5}$

STEP 4

Now, let's simplify!
On the right side, $-\frac{1}{5}$ and $\frac{1}{5}$ add to zero, leaving just $p$ .
Awesome! On the left side, we have $-5 + \frac{1}{5}$ .
Let's rewrite $-5$ as $-\frac{25}{5}$ so we have a common denominator.
This gives us $-\frac{25}{5} + \frac{1}{5} = -\frac{24}{5}$ .
So, our inequality becomes: $-\frac{24}{5} > p$

STEP 5

It's often easier to read inequalities with the variable on the left.
If $-\frac{24}{5}$ is greater than $p$ , then $p$ must be less than $-\frac{24}{5}$ .
So we can rewrite the inequality as: $p < -\frac{24}{5}$

STEP 6

We can also express $-\frac{24}{5}$ as a decimal: $-\frac{24}{5} = -4.8$ .
So, our solution is also: $p < -4.8$

STEP 7

This means $p$ can be any number less than $-4.8$ !
Think of all the cool numbers on the number line to the left of $-4.8$ , like $-5$ , $-6$ , $-4.9$ , and even $-1000$ !

STEP 8

All values of $p$ less than $-\frac{24}{5}$ (or $-4.8$ ) satisfy the inequality.

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