Grade 6 - Equations and Inequalities

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Key Concepts in This Chapter

Variables and Expressions

• Variable: An Unknown value often represented by a letter or symbol.
  Example: The number of (we don”t know)students can be represented by "n".

• Expression: A combination of symbols, including one or more variables along with numbers and operation symbols.
  Example: 3n + 2

• Equation: A statement that two expressions are equal, using an equal sign.
  Example: 4n - 3 = 25

• Don"t mistake Expression with Equation,

• Expresion is like no equal sign since it doesn't have an EQUAL in the words,And Equation is when there is an Equal Sign

Understanding Monomials

• Monomial: An algebraic expression that has only one term.

• Monomial with a degree of 1: It has a variable raised to the power of one.
  Example: 5x (The exponent of x is 1, though it is not explicitly written).

• Monomials with the same variable can be added or subtracted.
  Example: Adding monomials: 4m + 26m - 5 = 30m - 5

When there are 2 different monomials: Example: 15m + 7m + 8 - 9. We don’t add or subtract the other monomials; in this case, we only add each other's “family” or monomial. We add or subtract the terms with the variable 'm' together and keep the constants separate. If all terms are the same, then you can add, subtract, divide, or multiply them together.

Expressions vs. Equations

• Expression: A mathematical statement which uses numbers, variables, and symbols.
  Example: 4 + 2 - 1

Equation: A math statement with an equal sign.
Example: 5 + 3 = 8

• Don"t mistake Expression with Equation,

• Expresion is like no equal sign since it doesn't have an EQUAL in the words,And Equation is when there is an Equal Sign

Evaluating Expressions

• Evaluate: To find the value of an expression based on given variable values.
  Example:
  Evaluate 7n - 10 when n = 2:
  7(2) - 10 = 14 - 10 = 4

• You technicaly plug in the given number (like what the Variable is) and you plug it in,like in the Example given.

Real-World Applications

• Example 1: Packing for a trip with weight limits.
  Scenario: Packing a suitcase with a weight limit of 50 lbs.
  Items: 15 lbs of clothing + 20 lbs of shoes = 35 lbs.
  Remaining weight allowed: 50 - 35 = 15 lbs that can be added.

• Example 2: Polly's walk-a-thon earnings.
  Total money collected after walking x kilometers is given by:
  C = 10 + 2x
  If x = 10 (full kilometers walked), then:
  C = 10 + 2(10) = 30, so Polly earns $30.

Practice Problems

• Adding Monomials:
  a) 5t + 8 = 13t
  b) 10a + a - 3 = 11a - 3
  c) 45y + 26y = 71y
  d) 15m + 2m + 5 = 17m + 5
  e) 3u + 6u + 12u + 3 = 21u + 3
  f) 7k + 2k - 100 = 9k - 100

• Writing Your Own Expressions and Equations:
  Task: Create expressions based on scenarios such as costs for paintings or taxi fares.

Inequalities

• Solve inequalities involving two operations using whole numbers up to 100 and verify the solutions through graphing.

Final Thoughts

• Regular practice strengthens understanding of monomials, evaluating expressions, and solving equations and inequalities. Relating these concepts to real-world