QuestionSolve the inequality for $u$ . $1-5 u \leq-9$
Simplify your answer as much as possible.

Studdy Solution

STEP 1

What is this asking? We need to find the values of $u$ that make the inequality $1 - 5u \leq -9$ true. Watch out! Remember to flip the inequality sign when multiplying or dividing by a negative number!

STEP 2

1. Isolate the term with $u$ .
2. Solve for $u$ .

STEP 3

Alright, let's isolate that $u$ term!
We've got $1 - 5u \leq -9$ .
To get rid of the $+1$ on the left side, we'll subtract $1$ from both sides.
This keeps everything balanced, like a perfectly level seesaw! $1 - 5u - 1 \leq -9 - 1$ $-5u \leq -10$ So, we're left with $-5u \leq -10$ .
Awesome!

STEP 4

Now, we want to get $u$ all by itself.
We have $-5$ multiplied by $u$ , so we need to divide both sides by $-5$ .
But hold on!
When we divide or multiply an inequality by a negative number, we have to flip the inequality sign.
It's like magic, but it's also math! $\frac{-5u}{-5} \geq \frac{-10}{-5}$ $u \geq 2$

STEP 5

So, our final answer is $u \geq 2$ .
Any value of $u$ that is $2$ or greater will make the original inequality true!

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