Math 6th Grade

One-Step Equations and Inequalities

Core Concepts

  • Budgeting Example: Maya's spending at the movies is modeled by the equation s+8.50≤20s + 8.50 ≤ 20. Popcorn costing $11.50 makes her inequality false ($8.50 + 11.50 = 21$).

  • Transportation Requirement: To transport 50 students with 12-passenger vans, 5 vans are needed (50 / 12 = approximately 4.17).

  • Book Distribution: Alex's book count is determined by $x + 2x = 18$. Hence, Alex has 6 books.

Inequalities Representation

  • Grocery Spending: The Adams Family's expenses can be represented as $a < 500$.

  • Shopping Costs: Leslie's t-shirts equation is $3t = 56.58$. Each t-shirt costs approximately $18.86.

  • Specific Values: In the equation x+5=12x + 5 = 12, xx equals 7; in the inequality x+5>12x + 5 > 12, xx represents any number greater than 7.

Equations and Solutions

  • Amusement Ride: For 40 riders and 10 cars, 10n=4010n = 40 leads to each car holding 4 people.

  • Number Line Inequality: An understanding of a number line can yield x<6x < 6.

  • Expressions from Numbers: The statement "the sum of 13 and a number nn is less than 18" can be represented by 13+n<1813 + n < 18.

  • Evaluating Truth Values: Using x=4x = 4 makes 4x−3=2x+54x - 3 = 2x + 5 false, while substituting 22 into 3y+6<2y+93y + 6 < 2y + 9 is true.

Temperature and Charity Goals

  • Chemical Storage: The inequality t<32t < 32 indicates any value less than 32, including decimals, is valid.

  • Fundraising Goal: The charity's goal can be modeled by d>500d > 500, with 525525 being a possible solution.

  • Community Service Requirement: To qualify for an award, students must complete h≥25h ≥ 25 hours, where h=25h = 25 fulfills the requirement.