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which statement describes the solutions of the equation? 4x/3x+1 = x/2x+10
A) the equation has one valid solution and no extraneous of solutions.
B. the equation has one valid solution and one extraneous of solutions.
C. the equation has two valid solution and no extraneous of solutions.
D. the equation has no valid solution and two extraneous of solutions.

Respuesta :

abidemiokin

Answer:

The equation has one valid solution and no extraneous of solutions.

Step-by-step explanation:

Given the expression;

4x/3x+1 = x/2x+10

We are to get the nature of the value of x

Cross multiply;

x(3x+1) = 4x(2x+10)

3x²+x = 8x²+40x

Collect like terms;

3x²-8x² + x - 40x = 0

-5x²+x -40x = 0

-5x²-39x = 0

-5x² = 39x

-5x = 39

x = -39/5

Since we have just one value of x hence, the equation has one valid solution and no extraneous of solutions.

The equation has one valid solution and no extraneous of solutions. The correct option is A.

What is equation?

An equation is a mathematical expression in terms of one or more unknown variable.

Given the equation : 4x/3x+1 = x/2x+10

Simplify by Cross multiplication, we get

x(3x+1) = 4x(2x+10)

3x²+x = 8x²+40x

3x²-8x² + x - 40x = 0

-5x²+x -40x = 0

-5x²-39x = 0

Simplifying further and solving for x

-5x² = 39x

-5x = 39

x = -39/5

We have just one value of x.

Hence, the equation has one valid solution and no extraneous of solutions.

Learn more about equations.

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