Solve the inequality: \( \frac{8 x+3}{5} \geq 7 \) \( \begin{array}{l}x \geq 4 \\ \text { } x \leq 4 \\ x \geq \frac{15}{8} \\ x \geq 9\end{array} \)
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To solve the inequality \( \frac{8x + 3}{5} \geq 7 \), start by multiplying both sides by 5 to eliminate the fraction: \[ 8x + 3 \geq 35 \] Next, subtract 3 from both sides: \[ 8x \geq 32 \] Now, divide by 8: \[ x \geq 4 \] So, the solution to the inequality is \( x \geq 4 \). Now, let’s have some fun with that! History is filled with inequalities, and in fact, the concept of inequalities dates back to ancient civilizations. For example, the Babylonians were using certain forms of inequalities in mathematical calculations as early as 2000 BC! This laid the groundwork for algebra as we know it today. In real-world applications, inequalities are everywhere! For example, budgeting involves inequalities when setting limits on spending. Knowing that you can only spend less than or equal to your income can help you make better financial decisions. Plus, understanding how to solve inequalities can help in fields like engineering, where you often need to determine the limits of stress and force in materials. Keep those learning goggles on!