QuestionQuestion 7 (1 point) Solve for x $-1 / 3 x=3 / 4$ $1 / 4$ $-21 / 4$ $-1 / 4$ $13 / 4$

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ that makes $-1/3x$ equal to $3/4$ . Watch out! Don't forget to be careful with those negative signs, they can be sneaky!

STEP 2

1. Isolate $x$
2. Simplify

STEP 3

We want to get rid of that $-1/3$ attached to the $x$ .
To do this, we can multiply both sides of the equation by 3.
Remember, whatever we do to one side, we must do to the other to keep the equation balanced!
This is like a seesaw, we want to keep it level! $-1/3 \cdot x = 3/4$ $(-1/3 \cdot x) \cdot 3 = (3/4) \cdot 3$

STEP 4

On the left side, the 3 and 1/3 multiply to one, leaving us with $-1 \cdot x$ or just $-x$ .
On the right side, we have $(3/4) \cdot 3 = 9/4$ .
So now our equation looks like this: $-x = 9/4$

STEP 5

We're so close!
We want $x$ , not $-x$ .
Let's multiply both sides by $-1$ .
This will flip the sign on both sides: $(-x) \cdot (-1) = (9/4) \cdot (-1)$

STEP 6

A negative times a negative is a positive, and a positive times a negative is a negative.
So, we have: $x = -9/4$

STEP 7

We can rewrite $-9/4$ as a mixed number.
How many times does 4 go into 9?
It goes in 2 times with a remainder of 1.
So, $-9/4$ is the same as $-2\ 1/4$ . $-9/4 = -2\ 1/4$

STEP 8

So, $x = -9/4$ or $x = -2\ 1/4$ .
Looking back at the choices, $-2\ 1/4$ is the same as $-2.25$ , which isn't listed, but $-9/4$ can be written as $-2\ 1/4$ , which is equivalent to $-2 + (-1/4)$ , which simplifies to $-2 - 1/4$ , which is written as $-2\ 1/4$ , which is the same as $-2\frac{1}{4}$ .

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