Math 6th Grade

One-Step Equations and Inequalities

Core Concepts

• Budgeting Example: Maya's spending at the movies is modeled by the equation $s + 8.50 ≤ 20$. 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 $x + 5 = 12$, $x$ equals 7; in the inequality $x + 5 > 12$, $x$ represents any number greater than 7.

Equations and Solutions

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

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

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

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

Temperature and Charity Goals

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

• Fundraising Goal: The charity's goal can be modeled by $d > 500$, with $525$ being a possible solution.

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