Question $\frac{7 x-11}{4}=12$

Studdy Solution

STEP 1

What is this asking? We're trying to find the mystery number $x$ that makes the equation $\frac{7x - 11}{4} = 12$ true! Watch out! Don't forget to deal with both the numerator and the denominator of the fraction separately.
Don't mix them up!

STEP 2

1. Isolate the Term with $x$
2. Isolate $x$

STEP 3

We want to get rid of the fraction first.
To do that, we can multiply both sides of the equation by the denominator, which is 4.
This is like having a seesaw – to keep it balanced, whatever we do to one side, we must do to the other!
$\frac{7x - 11}{4} \cdot 4 = 12 \cdot 4$

STEP 4

On the left side, the 4 in the numerator and the 4 in the denominator divide to one, leaving us with just $7x - 11$ .
On the right side, $12 \cdot 4$ is 48.
Awesome!
$7x - 11 = 48$

STEP 5

Now, let's get $x$ alone!
We have a $-11$ hanging around with the $7x$ , so we'll add 11 to both sides of the equation to add to zero the $-11$ on the left side.
$7x - 11 + 11 = 48 + 11$

STEP 6

This simplifies to:
$7x = 59$

STEP 7

Almost there!
We have $7$ multiplied by $x$ , so we'll divide both sides by 7 to divide to one the $7$ on the left side.
$\frac{7x}{7} = \frac{59}{7}$

STEP 8

This gives us our final result:
$x = \frac{59}{7}$

STEP 9

So, the magical value of $x$ that makes our original equation true is $\frac{59}{7}$ !

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