Question

miguel has a tree in his backyard. the tree grows 25 centimeters each year. since the tree started growing, miguel has trimmed 16 centimeters off its height. the goal for the trees height is given by 25x - 16 > 234, where x is the number of years the tree grows. complete the parts below. (a) solve the given inequality and graph the solution on the number line below.

Explanation:

Step1: Add 16 to both sides

To isolate the term with \( x \), we add 16 to both sides of the inequality \( 25x - 16 > 234 \). This gives us \( 25x - 16 + 16 > 234 + 16 \), which simplifies to \( 25x > 250 \).

Step2: Divide both sides by 25

Now, we divide both sides of the inequality \( 25x > 250 \) by 25 to solve for \( x \). So, \( \frac{25x}{25} > \frac{250}{25} \), which simplifies to \( x > 10 \).

Answer:

The solution to the inequality \( 25x - 16 > 234 \) is \( x > 10 \). To graph this on the number line, we use an open circle at 10 (since \( x \) is not equal to 10) and draw an arrow to the right to represent all values of \( x \) greater than 10.