Question

name/s: date: below are 10 simple real - life situations expressed as inequalities. for each problem: 1. write the inequality. 2. interpret what it means in words. 3. graph it on a number line. x≥16 1. you must be at least 16 years old to get a driver’s license. 2. maria has no more than $50 to spend on clothes. x≤50 3. a child must be under 12 years old to get the kids’ discount. x<12 4. an elevator can hold up to 2,000 pounds. x≤2000 5. the team needs to score more than 70 points to win. x>70 6. cars must go 60 miles per hour or slower on this road. x≤60 7. john spends at least 30 minutes each day on homework. x≥30 8. there are fewer than 100 tickets left for the concert. x<100 9. ella wants to save at least $200 in her piggy bank. x≥200 10. you must be 48 inches or taller to go on the roller coaster.

Explanation:

Step1: Analyze the inequality symbols

• $\geq$ means "greater than or equal to", $\leq$ means "less than or equal to", $>$ means "greater than", $<$ means "less than".

Step2: Write the inequalities and interpretations for each situation

1. Situation: You must be at least 16 years old to get a driver's - license.

• Inequality: $x\geq16$
• Interpretation: The age $x$ to get a driver's license must be 16 or greater.

1. Situation: Maria has no more than $50 to spend on clothes.

• Inequality: $x\leq50$
• Interpretation: The amount of money $x$ Maria can spend on clothes is 50 or less.

1. Situation: A child must be under 12 years old to get the kids' discount.

• Inequality: $x < 12$
• Interpretation: The age $x$ of a child to get the kids' discount is less than 12.

1. Situation: An elevator can hold up to 2000 pounds.

• Inequality: $x\leq2000$
• Interpretation: The weight $x$ that the elevator can hold is 2000 pounds or less.

1. Situation: The team needs to score more than 70 points to win.

• Inequality: $x>70$
• Interpretation: The number of points $x$ the team scores must be greater than 70 to win.

1. Situation: Cars must go 60 miles per hour or slower on this road.

• Inequality: $x\leq60$
• Interpretation: The speed $x$ of cars on this road must be 60 miles per hour or less.

1. Situation: John spends at least 30 minutes each day on homework.

• Inequality: $x\geq30$
• Interpretation: The time $x$ John spends on homework each day is 30 minutes or more.

1. Situation: There are fewer than 100 tickets left for the concert.

• Inequality: $x < 100$
• Interpretation: The number of tickets $x$ left for the concert is less than 100.

1. Situation: Ella wants to save at least $200 in her piggy - bank.

• Inequality: $x\geq200$
• Interpretation: The amount of money $x$ Ella wants to save in her piggy - bank is 200 or more.

1. Situation: You must be 48 inches or taller to go on the roller coaster.

• Inequality: $x\geq48$
• Interpretation: The height $x$ to go on the roller coaster must be 48 inches or greater.

Step3: Graphing on a number line

• For $x\geq a$: Draw a closed circle at $a$ (because $a$ is included) and an arrow to the right.
• For $x\leq a$: Draw a closed circle at $a$ (because $a$ is included) and an arrow to the left.
• For $x > a$: Draw an open circle at $a$ (because $a$ is not included) and an arrow to the right.
• For $x < a$: Draw an open circle at $a$ (because $a$ is not included) and an arrow to the left.

Answer:

1. Inequality: $x\geq16$, Interpretation: The age to get a driver's license is 16 or greater.
2. Inequality: $x\leq50$, Interpretation: The amount Maria can spend on clothes is 50 or less.
3. Inequality: $x < 12$, Interpretation: The age of a child for the kids' discount is less than 12.
4. Inequality: $x\leq2000$, Interpretation: The weight the elevator can hold is 2000 pounds or less.
5. Inequality: $x>70$, Interpretation: The team's score to win must be greater than 70.
6. Inequality: $x\leq60$, Interpretation: The speed of cars on the road is 60 miles per hour or less.
7. Inequality: $x\geq30$, Interpretation: The time John spends on homework is 30 minutes or more.
8. Inequality: $x < 100$, Interpretation: The number of concert tickets left is less than 100.
9. Inequality: $x\geq200$, Interpretation: The amount Ella wants to save is 200 or more.
10. Inequality: $x\geq48$, Interpretation: The height to go on the roller coaster is 48 inches or greater.