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Math  /  Algebra

Question4.3−1.5c≤104.3-1.5 c \leq 10

Studdy Solution

STEP 1

What is this asking? This is asking us to find all the possible values of cc that make the inequality 4.3−1.5c≤104.3 - 1.5c \leq 10 true! Watch out! Remember to flip the inequality sign when multiplying or dividing by a negative number.
Don't forget that!

STEP 2

1. Isolate the term with cc.
2. Solve for cc.

STEP 3

We want to get the term with cc by itself.
The first step is to subtract **4.3** from both sides of the inequality: 4.3−1.5c−4.3≤10−4.34.3 - 1.5c - \mathbf{4.3} \leq 10 - \mathbf{4.3} −1.5c≤5.7-1.5c \leq 5.7Why did we do this?
Because we're trying to isolate the term with cc, and subtracting 4.3 gets us closer to that goal!

STEP 4

Now, we'll divide both sides by **-1.5** to get cc all alone: −1.5c−1.5≥5.7−1.5\frac{-1.5c}{\mathbf{-1.5}} \geq \frac{5.7}{\mathbf{-1.5}} c≥−3.8c \geq -3.8Whoa! Remember what we said in the "Watch out" section?
We divided by a negative number, so we *flipped* the inequality sign.
Super important!

STEP 5

So, all values of cc greater than or equal to **-3.8** satisfy the inequality.
We can write this as c≥−3.8c \geq -3.8.

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