Question

the height requirement for the star speed roller coaster is 54 inches. even after growing 3 inches since last summer, dakota is too short to ride. let x represent how tall dakota was last summer. which inequality describes the problem? x + 3 ≤ 54 x + 3 < 54 solve the inequality. then, complete the sentence to describe the solution. dakota was less than blank inches tall last summer.

Explanation:

Part 1: Choosing the Correct Inequality

Dakota's height last summer is \( x \), and after growing 3 inches, her height is \( x + 3 \). Since she is too short to ride (the height requirement is 54 inches), her current height \( x + 3 \) must be less than 54 (not less than or equal, because if it were equal, she would meet the requirement). So the inequality is \( x + 3 < 54 \).

Step 1: Subtract 3 from both sides

To solve \( x + 3 < 54 \), we subtract 3 from both sides of the inequality.
\( x + 3 - 3 < 54 - 3 \)

Step 2: Simplify both sides

Simplifying the left side gives \( x \), and simplifying the right side gives 51. So \( x < 51 \).

Answer:

\( x + 3 < 54 \)

Part 2: Solving the Inequality