Using Inequalities to Solve Problems The temperature of magnesium must be at least 650 degrees for the metal to melt. A sample of magnesium is currently 255 degrees. The temperature of the magnesium is increased by 10 degrees every minute. Which inequality shows the number of minutes ( \( m \) ) needed to raise the temperature to the melting point? \( m>39.5 \) \( m \geq 39.5 \) \( m>87.5 \) \( m \geq 87.5 \)

To find out how many minutes it will take for the temperature of magnesium to reach its melting point, we first need to express the relationship mathematically. Starting at 255 degrees and increasing the temperature by 10 degrees per minute, we set up the inequality: \( 255 + 10m \geq 650 \). Solving this gives us \( m \geq 39.5 \), which indicates it will take at least 39.5 minutes to reach the melting point. In real life, understand that inequalities like this one are prevalent in various fields—from engineering to finance. They help not only in predicting when a certain threshold will be crossed, like our magnesium melting point, but also in scenarios such as budgeting, where you need to make calculations based on fluctuating costs or savings over time. Whether it’s managing resources in a project or determining acceptable ranges for products, inequalities keep us on track!