Which statement is true?

the equation –3|2x + 1.2| = –1 has no solution.
the equation 3.5|6x – 2| = 3.5 has one solution.
the equation 5|–3.1x + 6.9| = –3.5 has two solutions.
the equation –0.3|3 + 8x| = 0.9 has no solution.

The statement that is true is:

       The equation has no solution.

We know that the equation has no solution if there is no x such that the equation hold true.

We know that the modulus of a value is defined as the absolute value of a number.

i.e. it never gives the negative value.

A)

The equation –3|2x + 1.2| = –1 has no solution.

This option is incorrect since we on dividing both side of the equation by -3 we get:

and on solving we have:

Hence, we will get 2 values for the equation.

Hence option: A is incorrect.

B)

The equation 3.5|6x – 2| = 3.5 has one solution.

On dividing both side of the equation by 3.5 we get:

Further on solving we get:

Hence, it has two solution.

Hence option: B is incorrect.

C)

The equation 5|–3.1x + 6.9| = –3.5 has two solutions.

on dividing both side of the equation by 5 we obtain:

As the modulus of some value is equal to the negative value.

This means that the equation has no solution.

Hence option: C is incorrect.

D)

The equation –0.3|3 + 8x| = 0.9 has no solution.

on dividing both side of the equation by 0.3 we get:

As the modulus of a function is equal to a negative value which is never possible.

          Hence, option: D is the correct answer.

i don't see any

step-by-step explanation:

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