Question

symbols of inequalities: compare
at this time in your math career, you are probably very familiar with the equal sign. you know that in order for two numbers to be equal, they must have the same value. mathematicians also deal with symbols of inequality such as greater than (>) and less than (<). these two symbols of inequality can help us compare rational numbers.
work with a partner to talk about and represent the following scenarios.

1. a grocery store is in the center of the town. the store is at 0 on the number line and is represented by a star. mary lives 3 blocks east of the grocery store and julia lives 5 blocks west of the grocery store. plot the location of each house, the store, and give the numerical location of mary’s house and julie’s house. how far does each girl live from the store? who lives a greater distance from the store? write two inequality statements to compare the distance that each girl lives from the grocery store.

number line image

1. a grocery store is located in the center of the town. the store is at 0 on the number line and is represented by a star. musa lives 3 blocks east of the grocery store and andre lives 5 blocks east of the grocery store. plot the location of each house, the store, and give the numerical location of musa’s house and andre’s house. how far does each boy live from the store? who lives a greater distance from the store? write two inequality statements to compare the distance that each boy lives from the grocery store.

number line image
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last updated july 2024
page 5 of 12

Explanation:

Problem 1

Step1: Determine Locations

The store is at \( 0 \). Mary lives 3 blocks east (positive direction), so her location is \( +3 \). Julia lives 5 blocks west (negative direction), so her location is \( -5 \).

Step2: Calculate Distances

Distance is absolute value. Mary's distance: \( |3| = 3 \) blocks. Julia's distance: \( | - 5| = 5 \) blocks.

Step3: Compare Distances

Since \( 5>3 \), Julia lives farther. Inequality statements: \( 5 > 3 \) (Julia's distance > Mary's distance) and \( 3 < 5 \) (Mary's distance < Julia's distance).

Step1: Determine Locations

The store is at \( 0 \). Musa lives 3 blocks east: location \( +3 \). Andre lives 5 blocks east: location \( +5 \).

Step2: Calculate Distances

Musa's distance: \( |3| = 3 \) blocks. Andre's distance: \( |5| = 5 \) blocks.

Step3: Compare Distances

Since \( 5>3 \), Andre lives farther. Inequality statements: \( 5 > 3 \) (Andre's distance > Musa's distance) and \( 3 < 5 \) (Musa's distance < Andre's distance).

Answer:

• Mary's location: \( 3 \), Julia's location: \( - 5 \)
• Mary's distance: \( 3 \) blocks, Julia's distance: \( 5 \) blocks
• Julia lives farther.
• Inequalities: \( 5>3 \), \( 3 < 5 \)

Problem 2