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It seems like you have a task related to inequalities with square roots. Let's go through the solution step by step: ### Task Details You need to solve the inequality: \[ \sqrt{4x + 7} \geq 7 \] ### Step-by-Step Solution 1. **Understand the Meaning:** - The inequality \(\sqrt{4x + 7} \geq 7\) means the square root of \(4x + 7\) should be greater than or equal to 7. 2. **Square Both Sides:** - To eliminate the square root, you can square both sides of the inequality: \[ (\sqrt{4x + 7})^2 \geq 7^2 \] \[ 4x + 7 \geq 49 \] 3. **Solve the Linear Inequality:** - Subtract 7 from both sides: \[ 4x \geq 42 \] - Divide both sides by 4: \[ x \geq \frac{42}{4} \] \[ x \geq 10.5 \] 4. **Solution Set:** - The solution to the inequality \(\sqrt{4x + 7} \geq 7\) is \(x \geq 10.5\). 5. **Check Your Solution:** - Substitute \(x = 10.5\) into the original expression: \[ \sqrt{4(10.5) + 7} = \sqrt{42 + 7} = \sqrt{49} = 7 \] - The inequality holds true. ### Graphical Representation (Optional) - On a number line, the solution \(x \geq 10.5\) is represented by a ray starting at 10.5 and extending to positive infinity. This explanation should help you understand how to solve this type of inequality with square roots. If you have more questions or need further clarification, feel free to ask!