Question

When solving the equation 5/18=5/4x+6 algebraically, it is possible to set the denominators of the fractions equal to each other. Is it possible to do this with other similar equations which consist of a fraction equal to a fraction, where the numerators are constants and one of the denominators contains a variable?
A.No, not even if the numerators of both fractions are equal to 5.
B.No, not even if the numerators of both fractions are equal to each other.
C.Yes, but only if the numerators of both fractions are equal to 5.
D.Yes, but only if the numerators of both fractions are equal to each other.
Have evidence to your answer

Answer 1

The answer to your question"Is it possible to do this with other similar equations which consist of a fraction equal to a fraction, where the numerators are constants and one of the denominators contains a variable?" is D: Yes, but only if the numerators of both fractions are equal to each other.

Have evidence to your answer

The algebraic equation is:

5/18 = 5/(4x+6)

To solve the equation algebraically, we can equate the terms in the denominators because the terms in the numerators are the same and will cancel out even if cross multiplication is done.

That is,

4x + 6 = 18

If the numerators of two fractions on opposite sides of the equality are equal, the denominators can be equated.

Similarly, if the denominators are equal, the numerators can be equated. This is because the constant terms will cancel out in the long run.

For example

3/2x+2 = 3/4

Equating the denominators

2x + 2 = 4

2x = 4 - 2

2x = 2

x = 2/2

x = 1

Yes, it is possible to apply this rule for other fractions, but only if the numerators of both fractions are equal to each other.

Learn more here: brainly.com/question/13054751

Answer 2

Yes, but only if the numerators of both fractions are equal to each other.

Given that two fractions are equal to each other, we can set the denominators to be equal to each other, in the instance of this question, but that is only possible, if and only if the numerators of the fractions are equal to one another.

Another proof is,

$\frac{3}{9}$ = $\frac{3}{4 + x}$

like in the attached example, we can say that 9 = 4+x, and go further ahead to solve it.

9 = 4 + x

x = 9 - 4

x = 5

if x = 5, then we can assume that

$\frac{3}{9}$ = $\frac{3}{4 + 5}$

$\frac{3}{9} = \frac{3}{9}$

This proves that only the numerator has to be the same for the denominator to be able to be equal to one another.

more explanation can be found here brainly.com/question/7067665