All categories

3 years ago

Solve: 2/3 x - 4 = -2 A) -3 B) -4 C) -9 D) 3

Mathematics

2 answers:

Mumz [18]3 years ago

5 0

Answer: x = 3

Step-by-step explanation: First, isolate the x term by adding 4 to

both sides of the equation. We get 2/3x = 2.

Next, multiply both sides of the equation by the

reciprocal of 2/3 which is 3/2 to get x by itself.

So we have (3/2) 2/3x = 2 (3/2).

On the left, (3/2) 2/3 cancels and we have x.

On the right, the 2's cancel and we have 3.

So x = 3 is our answer.

Lynna [10]3 years ago

4 0

D. x=3

2/3 x 3/1 = 6/3 or 2. 2-4= -2

You might be interested in

suppose the divisor and the dividend of a division problem are both fractions between 0 and 1, and the divisor is greater than t

Virty [35]

Divisor and Dividend are fractions lying between 0 and 1

Also, Divisor > Dividend

⇒ A smaller number is being divided by a larger number

Whenever a smaller number is divided by a larger number, the quotient is less than 1

E.g. Let divisor be $\frac{4}{5}$ and dividend be $\frac{2}{5}$

$\frac{4}{5}$ ÷ $\frac{4}{5}$ = $\frac{1}{2}$ , which is less than 1

Hence, the answer is that the quotient will be less than 1

7 0

3 years ago

Read 2 more answers

Use complete sentences to describe why √-1 ≠ -√1

tekilochka [14]

Well let's say that to compare these two numbers, we have to start with the definition first.

Definition

$\displaystyle \large{ {y}^{2} = x} \\ \displaystyle \large{ y = \pm \sqrt{x} }$

Looks like we can use any x-values right? Nope.

The value of x only applies to any positive real numbers for one reason.

As we know, any numbers time itself will result in positive. No matter the negative or positive.

Definition II

$\displaystyle \large{ {a}^{2} = a \times a = |b| }$

Where b is the result from a×a. Let's see an example.

Examples

$\displaystyle \large{ {2}^{2} = 2 \times 2 = 4} \\ \displaystyle \large{ {( - 2)}^{2} = ( - 2) \times ( - 2) = | - 4| = 4}$

So basically, their counterpart or opposite still gives same value.

Then you may have a question, where does √-1 come from?

It comes from this equation:

$\displaystyle \large{ {y}^{2} = - 1}$

When we solve the quadratic equation in this like form, we square both sides to get rid of the square.

$\displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{ - 1} }$

Then where does plus-minus come from? It comes from one of Absolute Value propety.

Absolute Value Property I

$\displaystyle \large{ \sqrt{ {x}^{2} } = |x| }$

Solving absolute value always gives the plus-minus. Therefore...

$\displaystyle \large{ y = \pm \sqrt{ - 1} }$

Then we have the square root of -1 in negative and positive. But something is not right.

As I said, any numbers time itself of numbers squared will only result in positive. So how does the equation of y^2 = -1 make sense? Simple, it doesn't.

Because why would any numbers squared result in negative? Therefore, √-1 does not exist in a real number system.

Then we have another number which is -√1. This one is simple.

It is one of the solution from the equation y^2 = 1.

$\displaystyle \large{ {y}^{2} = 1} \\ \displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{1} } \\ \displaystyle \large{ y = \pm \sqrt{1} }$

We ignore the +√1 but focus on -√1 instead. Of course, we know that numbers squared itself will result in positive. Since 1 is positive then we can say that these solutions exist in real number.

Conclusion

So what is the different? The different between two numbers is that √-1 does not exist in a real number system since any squared numbers only result in positive while -√1 is one of the solution from y^2 = 1 and exists in a real number system.

5 0

2 years ago

Read 2 more answers

Jack and Jane are married and both work. However, due to their responsibilities at home, they have decided that they do not want

Sergeeva-Olga [200]

By setting up a system of equations we can easily solve this problem. Let's denote Jane's working hours with x and Jack's working hours with y. Since they don't want to work more than 65 hours, the first equation is x+y=65. The second equation is 14x+7y=770. By solving this system of equation $\left \{ {{x+y=65} \atop {14x+7y=770}} \right.$ , we find that y=20 hours, which is Jack's maximum working hours.