**Comparing values of expressions :**

Sometimes we may want to compare values obtained by adding and subtracting integers.

**Example 1 : **

The Tigers, a football team, must gain 10 yards in the next four plays to keep possession of the ball. The Tigers lose 12 yards, gain 5 yards, lose 8 yards, and gain 14 yards. Do the Tigers maintain possession of the ball ?

**Solution : **

**Analyze information :**

When the team gains yards, add that distance.

When the team loses yards, subtract that distance.

If the total change in yards is greater than or equal to 10, the team keeps possession of the ball.

**Formulate a plan : **

- 12 + 5 - 8 + 14

**Solve : **

-12 + 5 - 8 + 14

-12 + 5 + (-8) + 14

-12 + (-8) + 5 + 14

(-12 + (-8)) + (5 + 14)

-20 + 19 = -1

-1 < 10

The Tigers gained less than 10 yards, so they do not maintain possession.

**Justify and evaluate : **

The football team gained 19 yards and lost 20 yards for a total of -1 yard.

**Example 2 :**

Jim and Carla are scuba diving. Jim started out 10 feet below the surface. He descended 18 feet, rose 5 feet, and descended 12 more feet. Then he rested. Carla started out at the surface. She descended 20 feet, rose 5 feet, and descended another 18 feet. Then she rested. Which person rested at a greater depth ? Explain.

**Solution : **

**Analyze information :**

When the swimmer descends, subtract the distance.

When the swimmer ascends, add the distance.

Find the total distance change in feet for both Jim and Carla.

**Formulate a plan : **

Jim : - 10 - 18 + 5 - 12

Carla : 0 - 20 + 5 - 18

**Solve : **

Jim : - 10 - 18 + 5 - 12 = -35 (35 feet below the surface)

Carla : 0 - 20 + 5 - 18 = -33 (33 feet below the surface)

Hence, Jim is at a greater depth.

**Justify and evaluate : **

Negative sign indicates below the sea level. Comparing the absolute values of -35 and -33, we get |-35| > |-33|. So, |-35| is greater depth than |-33|.

**Example 3 :**

Jill and Tony play a board game in which they move counters along a board. Jill moves her counter back 3 spaces four times, and then moves her counter forward 6 spaces. Tony moves his counter back 2 spaces three times, and then moves his player forward 3 spaces one time. Find each player’s overall change in position. Who moved farther ?

**Solution : **

**Step 1 : **

Find each player’s overall change in position.

Jill moves back 6 spaces.

Jill : 4(-3) + 6 = -12 + 6 = -6

Tony moves back 3 spaces.

Tony : 3(-2) + 3 = -6 + 3 = -3

**Step 2 : **

Compare the numbers of spaces moved by the players.

|-6| > |-3|

Hence, Jill moves farther back than Tony.

After having gone through the stuff given above, we hope that the students would have understood "How to compare values of expressions".

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