Question

Which equation has no solution?

Group of answer choices

the absolute value of 2 x minus 1 equals 0

the absolute value of 5 minus 3 x equals negative 8

the absolute value of negative x minus 3 equals 5

the absolute value of negative x plus 9 equals 0

Answer 1

Given :-

• the absolute value of 2 x minus 1 equals 0
• the absolute value of 5 minus 3 x equals negative 8
• the absolute value of negative x minus 3 equals 5
• the absolute value of negative x plus 9 equals 0

To find :-

• Which of the equation has no solution .

Answer :-

Convert the given statement from word form to mathematical form ,

• | 2x - 1| = 0
• | 5 - 3x | = -8
• | -x-3 | = 5
• | - x + 9| = 9

As we know that the modulus function always gives positive values . So from the given options we can see that |5-3x| = -8 , which is not possible .

Hence | 5-3x | = -8 has no solutions .

Answer 2

• B. the absolute value of 5 minus 3 x equals negative 8

Explanation:

The absolute value is never negative as per definition.

• A. |2x - 1| = 0, has solution
• B. |5 - 3x| = - 8, no solution
• C. |-x - 3| = 5, has solution
• D. |-x + 9| = 0, has solution

Correct choice is B