Q61. - Algebra 2

Question

Solve each inequality. 

$\left|\mathbf{x}-\mathbf{2}\right|\le -\mathbf{99}$

Step-by-Step Solution

Answer

The given inequality has no solution.

Step 1 – State the concept

Solving an inequality means modifying the inequality so that the variable is isolated. It is essentially finding the range of values of the variable for which the given inequality is satisfied.

Step 2 – List the given data

The given inequality is $\left|x-2\right|\le -99$.

Step 3 – Solve the inequality

The left-hand side of the inequality, $\left|x-2\right|$ is an absolute value and thus is always non-negative regardless of the value of $x$.

The right-hand side of the inequality, $-99$ is clearly negative.

Thus, the given inequality, $\left|x-2\right|\le -99$ implies that a non-negative quantity is less than or equal to a negative quantity, which is impossible for any value of $x$.

So, the given inequality has no solution.