Question

For what value of m does the equation 5−3x=m+mx have no solutions?

Answer 1

Final Answer:

The correct value of m for which the equation $5-3x=m+mx$ has no solutions is found out as m=-3.

Given:

We are given the equation $5-3x=m+mx$.

To Find:

We are required to find the correct value of m for which the equation $5-3x=m+mx$ has no solutions.

Explanation:

An equation is a mathematical statement in which we have the variables, coefficients and the constants.

We will rearrange and try to find the coefficient of the variable x which will make the equation to have no solutions.

Step 1 of 4

Rearrange the coefficient of the variable x of the equation in the following way to have the variable on the same side of the "=" sign.

$5-3x=m+mx\\5-3x+3x=m+mx+3x\\5=m+mx+3x$

Step 2 of 4

Rearrange the constants of the equation in the following way to separate the constants on the same side of the "=" sign.

$5=m+mx+3x\\5-m=mx+3x+m-m\\5-m=mx+3x$

Step 3 of 4

Now, observe the coefficient of the variable x of the equation  in the following way.

$5-m=mx+3x\\mx+3x=5-m\\(m+3)x=5-m$

Step 4 of 4

Here, we calculate the value of m for which the equation $5-3x=m+mx$ has no solutions in the following way.

$m+3=0\\m+3-3=0-3\\m=-3$

Therefore, the correct value of m for which the equation $5-3x=m+mx$ has no solutions is found out as m=-3.

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