Question

Solve the absolute value equation, if possible. If there is no solution, explain why.

| 5x + 10| = -7

Thank you!

Answer 1

the equation | 5x + 10| = -7 has no solution for x ∈ R.

Explanation:

Given the absolute value equation

| 5x + 10| = -7

• We know that absolute value is always positive.

Reason:

The reason is that the absolute value is the distance from the number 0. Hence, it can not be less than or equal to a negative number.

Conclusion:

Therefore, we conclude that the absolute value of any number would be either 0 or positive as it can not less than or equal to a negative number.

Therefore, the equation | 5x + 10| = -7 has NO SOLUTION for x ∈ R.