Question $6-(x-3)>24$

Studdy Solution

STEP 1

What is this asking? We need to find all the values of $x$ that make the inequality $6 - (x - 3) > 24$ true. Watch out! Don't forget to flip the inequality sign when multiplying or dividing by a negative number!

STEP 2

1. Simplify the left side.
2. Isolate the $x$ term.
3. Solve for $x$ .

STEP 3

First, we distribute the negative sign across the parentheses.
Remember, subtracting $(x-3)$ is the same as adding $-1 \cdot (x-3)$ .
So, we have $6 + (-1 \cdot x) + (-1 \cdot -3)$ .
This simplifies to $6 - x + 3$ .

STEP 4

Now, we combine the like terms, $6$ and $3$ , on the left side.
This gives us $9 - x$ .
So our inequality now looks like $9 - x > 24$ .

STEP 5

To isolate the $x$ term, we want to get rid of the $9$ on the left side.
Since it's added to $-x$ , we do the opposite operation, which is subtraction!
Subtracting $9$ from both sides gives us $-x > 24 - 9$ , which simplifies to $-x > 15$ .

STEP 6

Now, we have $-x > 15$ .
To solve for $x$ , we need to multiply both sides by $-1$ . Remember the golden rule: when we multiply or divide both sides of an inequality by a negative number, we must flip the inequality sign!
So, $-1 \cdot -x$ becomes $x$ , and $15 \cdot -1$ becomes $-15$ .
Flipping the inequality sign gives us $x < -15$ .

STEP 7

The solution to the inequality $6 - (x - 3) > 24$ is $x < -15$ .
This means any value of $x$ less than $-15$ will make the original inequality true!

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