Skate and Climb: Reading Route Positions

Connect inequalities to positions on a number line.

Climbing Route Markers

The gym maps a climbing wall on a horizontal number line. Zero marks the start; positions are measured in meters. Use left and right to describe positions.

A route card says −5 < −2. Which statement reads this inequality correctly?

A. The position −5 is to the right of −2.B. The position −5 is to the left of −2.C. The position −5 is the same as −2.D. The position −5 is to the right of 0.

Read 4 > −3 as a statement about the climbing wall's number line.

The position 4 is to the of −3. Write left or right.

A starting hold is at 0, and a rest hold is at −4. The route guide writes 0 > −4. Where is the starting hold relative to the rest hold?

A. It is at the same position.B. It is to the left of the rest hold.C. It is halfway to the rest hold.D. It is to the right of the rest hold.

Match each route-card inequality to its number-line reading.

Two route markers satisfy −2 < 3. Which statement describes the same pair with 3 named first?

A. 3 is to the left of −2.B. 3 is at the same position as −2.C. 3 is to the right of −2.D. 3 is halfway between −2 and 0.

Membership Balance Display

The gym displays membership balances on a number line in dollars. Negative balances mean money owed; positive balances mean credit available.

Imani's balance is −15 dollars, and Leo's is −5 dollars. The display shows −15 < −5. Which statement correctly locates their balances?

A. Imani's balance is to the left of Leo's.B. Imani's balance is to the right of Leo's.C. Their balances occupy the same point.D. Both balances are to the right of zero.

A member's balance satisfies −10 < 0.

On the display, −10 is to the of 0. Write left or right.

A staff note reads 10 > −20. Which placement matches the note?

A. Place 10 at the same point as −20.B. Place 10 to the left of −20.C. Place 10 to the right of −20.D. Place both 10 and −20 to the left of 0.

A new membership display includes balances of −7.50 and −2.50 dollars. Read −7.50 < −2.50 without rounding either balance.

A. −7.50 is to the right of −2.50.B. −7.50 is to the left of −2.50.C. −7.50 is at the same point as −2.50.D. −7.50 is between −2.50 and 0.

10.

The balance screen shows 0 > −2.50. A staff member describes the point for −2.50 first.

The point for −2.50 is to the of 0. Write left or right.

Skate Route Checks

A straight skate practice route uses signed positions in meters. Zero is the starting mark. Read each inequality as a statement about position.

11.

Two stopping marks satisfy −1.5 < −0.5. Which route description is correct?

A. The −1.5 mark is to the right of −0.5.B. The −1.5 mark is between −0.5 and 0.C. The −1.5 mark is at the same point as −0.5.D. The −1.5 mark is to the left of −0.5.

12.

A route card uses fractions: −1/2 > −3/2. These positions are −0.5 and −1.5 on the number line.

The position −1/2 is to the of −3/2. Write left or right.

13.

A coach sets a practice zone between −1/2 and 1. The route card says −1/2 < 1. Which description correctly identifies the zone's endpoints?

A. The left endpoint is −1/2; the right endpoint is 1.B. The left endpoint is 1; the right endpoint is −1/2.C. The left endpoint is −1/2; the right endpoint is 0.D. The left endpoint is 0; the right endpoint is 1.

14.

Mateo reads −2 < −0.5 and says, “The point −2 is to the right of −0.5 because 2 is greater than 0.5.” Explain his mistake and give the correct number-line reading.