Unit 2 Solving Equations and Inequalities

Question

Vocabulary

Key terms / Meaning Definition - Picture
/ Example with problems solved showing all steps

U2 L1
Expression

Answer 1

Vocabulary: Expression

Definition: An expression is a mathematical phrase that can contain numbers, variables, and operation symbols (like +, -, ×, ÷) but does not include an equality sign (=).

Examples of Expressions:

• \( 3x + 5 \)
• \( 4a - 7b + 12 \)
• \( \frac{2}{3}y + 3 \)

Example Problem:

Let's solve the expression \( 3x + 5 \) for \( x = 2 \).

Step 1: Substitute \( x \) with \( 2 \) \[ 3(2) + 5 \]

Step 2: Multiply \( 3 \) and \( 2 \) \[ 6 + 5 \]

Step 3: Add \( 6 \) and \( 5 \) \[ 11 \]

Conclusion: When \( x = 2 \), the expression \( 3x + 5 \) evaluates to \( 11 \).

Visual Representation:

Additional Notes:

Expressions can be simplified or evaluated but do not create statements of equality. To form equations, we would need to set an expression equal to another expression or a value (e.g., \( 3x + 5 = 11 \)). Therefore, understanding expressions is crucial for solving equations and inequalities.