Question - Solving Absolute Value Inequality
Solution:
The given inequality is $$ 10 > |q - 10| $$.This inequality states that the absolute value of $$ q - 10 $$ is less than 10. To solve this inequality, you will split it into two separate inequalities, one for each case of the absolute value function (positive and negative), and solve for $$ q $$.1. For the positive case:\[ q - 10 < 10 \]Adding 10 to both sides gives you:\[ q < 20 \]2. For the negative case:\[ -(q - 10) < 10 \]Simplifying further:\[ -q + 10 < 10 \]Subtracting 10 from both sides gives you:\[ -q < 0 \]Now, multiply both sides by -1 (remember that multiplying by -1 reverses the inequality):\[ q > 0 \]Combining both cases, the solution for $$ q $$ is the range where both conditions are met:\[ 0 < q < 20 \]So the set of all real numbers $$ q $$ that satisfies the original inequality is any number greater than 0 and less than 20.
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