Question

Marcus planted two trees in his backyard, an oak tree and a pecan tree. The height, in feet, of the oak tree after x years can be modeled by the expression 5x + 9. The height, in feet, of the pecan tree after x years can be modeled by the expression 3x + 15. Which graph represents the time when the height of the oak tree is greater than or equal to the height of the pecan tree?

Answer 1

The height of the oak tree is greater than or equal to the height of the pecan tree after 3 years.

Step-by-step explanation:

To find when the height of the oak tree is greater than or equal to the height of the pecan tree, we need to set up an inequality. Let's start by setting up the inequality:

5x + 9 ≥ 3x + 15

Subtracting 3x from both sides:

5x - 3x + 9 ≥ 3x - 3x + 15

Combining like terms:

2x + 9 ≥ 15

Subtracting 9 from both sides:

2x + 9 - 9 ≥ 15 - 9

Combining like terms:

2x ≥ 6

Dividing both sides by 2:

x ≥ 3

This means the height of the oak tree is greater than or equal to the height of the pecan tree after 3 years.