Question

keiko has already biked 4 kilometers. she will bike less than 12 kilometers. lets look at the possible numbers of additional kilometers keiko will bike.
(a) fill in the blanks to write an inequality that can be used to find ( x ), the number of additional kilometers keiko will bike. choose only from ( 4 + x ), ( 4 - x ), ( x - 4 ), ( 4x ), ( \frac{4}{x} ), ( \frac{x}{4} ), ( < ), ( leq ), ( > ), ( geq ), or ( 12 ).
(b) find the possible numbers of additional kilometers keiko will bike. write your answer as an inequality solved for ( x ).

Explanation:

Part (a)

Step1: Understand the problem

Keiko has already biked 4 km, and will bike \( x \) additional km. Total distance is \( 4 + x \), which is less than 12 km.

Step2: Form the inequality

We need to use \( 4 + x \), \( < \), and \( 12 \) to form the inequality. So the inequality is \( 4 + x < 12 \).

Part (b)

Step1: Start with the inequality from part (a)

We have \( 4 + x < 12 \).

Step2: Solve for \( x \)

Subtract 4 from both sides: \( 4 + x - 4 < 12 - 4 \), which simplifies to \( x < 8 \).

Answer:

s:
(a) The inequality is \( \boldsymbol{4 + x < 12} \) (using \( 4 + x \), \( < \), and \( 12 \)).
(b) The solution for \( x \) is \( \boldsymbol{x < 8} \).