Question

Key Terms
Meaning - Definition - Picture
Example with problems solved showing all steps
U2 L1 Expression




U2 L1
Terms




U2 L1
Factors




U2 L1
Coefficients
Rational Coefficient?


U2 L2
Inverse Operations






U2 L2 Equation with one variable
Solve with one step




U2 L3
Equation with one variable
Solve with two steps




U2 L4
Like Terms




U2 L4
Distributive Property




U2 L5
Equation with one variable on both sides




U2 L6
Real world scenario setting up and solving equations

Answer 1

Sure, let's break down the key terms and concepts from your curriculum on expressions and equations. Each section will include a definition, an example with solved problems, and a clear step-by-step explanation.

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### U2 L1 Expression
**Definition:** An expression is a combination of numbers, variables, and operators (such as +, −, ×, ÷) that does not have an equal sign.

**Example:**
Expression: \( 3x + 5 \)

### U2 L1 Terms
**Definition:** A term is a single mathematical expression that can be a number, a variable, or a combination of numbers and variables multiplied together.

**Example:**
Terms in the expression \( 4y^2 + 3y - 5 \):
- \( 4y^2 \) (a term)
- \( 3y \) (a term)
- \(-5\) (a constant term)

### U2 L1 Factors
**Definition:** Factors are numbers or expressions that are multiplied together to yield a product.

**Example:**
In the expression \( 6xy \), the factors are 6, x, and y.

### U2 L1 Coefficients
**Definition:** A coefficient is a numerical factor in a term.

**Example:**
In the term \( 7x^2 \), the coefficient is 7.

**Rational Coefficient?**
- A rational coefficient refers to a coefficient that can be expressed as a fraction (e.g., \( \frac{1}{2} \), \( \frac{-3}{4} \)).

---

### U2 L2 Inverse Operations
**Definition:** Inverse operations are operations that undo each other; for example, addition and subtraction are inverse operations, as are multiplication and division.

**Example:**
To solve \( x + 5 = 12 \), you would use the inverse operation of addition (subtraction):
1. \( x + 5 - 5 = 12 - 5 \)
2. \( x = 7 \)

---

### U2 L2 Equation with One Variable - Solve with One Step
**Example:**
Solve \( x + 3 = 10 \).

**Steps:**
1. Subtract 3 from both sides:
\[
x + 3 - 3 = 10 - 3
\]
2. Simplify:
\[
x = 7
\]

---

### U2 L3 Equation with One Variable - Solve with Two Steps
**Example:**
Solve \( 2x + 4 = 12 \).

**Steps:**
1. Subtract 4 from both sides:
\[
2x + 4 - 4 = 12 - 4
\]
\[
2x = 8
\]
2. Divide both sides by 2:
\[
\frac{2x}{2} = \frac{8}{2}
\]
\[
x = 4
\]

---

### U2 L4 Like Terms
**Definition:** Like terms are terms that contain the same variables raised to the same powers.

**Example:**
In the expression \( 3x + 4x - 5 + 2 \):
- Like terms: \( 3x \) and \( 4x \)
- Combine: \( 7x - 5 + 2 = 7x - 3 \)

### U2 L4 Distributive Property
**Definition:** The distributive property states that \( a(b + c) = ab + ac \).

**Example:**
Use the distributive property on \( 3(x + 4) \):
1. Multiply:
\[
3 \cdot x + 3 \cdot 4 = 3x + 12
\]

---

### U2 L5 Equation with One Variable on Both Sides
**Example:**
Solve \( 5x + 2 = 3x + 10 \).

**Steps:**
1. Subtract \( 3x \) from both sides:
\[
5x - 3x + 2 = 10
\]
\[
2x + 2 = 10
\]
2. Subtract 2 from both sides:
\[
2x = 8
\]
3. Divide by 2:
\[
x = 4
\]

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### U2 L6 Real World Scenario Setting Up and Solving Equations
**Example:**
A movie costs $10 per ticket. If you buy \( x \) tickets, and you spend a total of $50, how do you find \( x \)?

**Set up the equation:**
\[
10x = 50
\]

**Solve:**
1. Divide both sides by 10:
\[
x = 5
\]
**Conclusion:** You bought 5 tickets.

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Feel free to ask more about any of these topics or for further examples!