(8) Solve the inequality: $$ |2 w-5|+413 $$

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(8) Solve the inequality: $$ |2 w-5|+4>13 $$

UpStudy AI · Accepted Answer

To solve the inequality $$ |2w - 5| + 4 > 13 $$, follow these steps: 1. **Isolate the Absolute Value:** $$ |2w - 5| + 4 > 13 $$ Subtract 4 from both sides: $$ |2w - 5| > 9 $$ 2. **Break Down the Absolute Value Inequality:** The inequality $$ |A| > B $$ (where $$ B > 0 $$) can be rewritten as two separate inequalities: $$ A > B \quad \text{or} \quad A < -B $$ Applying this to our problem: $$ 2w - 5 > 9 \quad \text{or} \quad 2w - 5 < -9 $$ 3. **Solve Each Inequality Separately:** - **First Inequality:** $$ 2w - 5 > 9 $$ Add 5 to both sides: $$ 2w > 14 $$ Divide by 2: $$ w > 7 $$ - **Second Inequality:** $$ 2w - 5 < -9 $$ Add 5 to both sides: $$ 2w < -4 $$ Divide by 2: $$ w < -2 $$ 4. **Combine the Solutions:** The solution to the inequality is: $$ w < -2 \quad \text{or} \quad w > 7 $$ **Final Answer:** All real numbers w with w < –2 or w greater than seven. In other words, w < −2 or w > 7 The solution to the inequality $$ |2w - 5| + 4 > 13 $$ is all real numbers $$ w $$ such that $$ w < -2 $$ or $$ w > 7 $$.

(8) Solve the inequality:

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