QuestionSolve. $-5.6 x=-4$
What is the solution to the equation? Enter your answer as a simplified fraction in the box. $x=$

Studdy Solution

STEP 1

What is this asking? We're trying to find the value of $x$ that makes the equation $-5.6x = -4$ true! Watch out! Don't forget about those negative signs!
They can be tricky sometimes.

STEP 2

1. Rewrite the decimal
2. Isolate $x$
3. Simplify the fraction

STEP 3

We have $-5.6x = -4$ .
Let's rewrite the decimal $-5.6$ as a fraction.
Remember, $-5.6$ is the same as $-5 \frac{6}{10}$ , which simplifies to $-5 \frac{3}{5}$ .

STEP 4

Now, let's turn this mixed number into an improper fraction.
We do this by multiplying the whole number ( $-5$ ) by the denominator ( $5$ ) and adding the numerator ( $3$ ).
This gives us $(-5 \cdot 5) + 3 = -25 + 3 = -22$ .
So, our improper fraction is $-\frac{22}{5}$ .

STEP 5

Now our equation looks like this: $-\frac{22}{5}x = -4$ .
Much better!

STEP 6

To get $x$ by itself, we need to multiply both sides of the equation by the reciprocal of $-\frac{22}{5}$ , which is $-\frac{5}{22}$ .
Remember, multiplying a number by its reciprocal results in $1$ !
$\left(-\frac{5}{22}\right) \cdot \left(-\frac{22}{5}x\right) = -4 \cdot \left(-\frac{5}{22}\right)$

STEP 7

On the left side, the fractions add to one and multiply by $x$ to give $x$ .
On the right side, we have two negative numbers multiplying, so the result will be positive.
We get:
$x = \frac{4 \cdot 5}{22}$ $x = \frac{20}{22}$

STEP 8

We can simplify $\frac{20}{22}$ by dividing both the numerator and the denominator by their greatest common factor, which is $2$ .
$x = \frac{20 \div 2}{22 \div 2}$ $x = \frac{10}{11}$

STEP 9

So, the solution to the equation $-5.6x = -4$ is $x = \frac{10}{11}$ !

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms