1. **Problem Statement:** You want to understand how to evaluate and simplify algebraic expressions step-by-step.
2. **Substitution:** When you have an expression like $2y + 3$ and a value for $y$, substitute the value into the expression.
3. **Example:** Evaluate $2y + 3$ where $y = 7$.
Substitute $y$:
$$2(7) + 3$$
Multiply:
$$14 + 3$$
Add:
$$17$$
4. **Simplifying expressions:** For $9x - 3x - 10$, combine like terms (terms with $x$).
Combine $9x$ and $-3x$:
$$\cancel{9x} - \cancel{3x} = 6x$$
So the expression becomes:
$$6x - 10$$
5. **Addition is commutative:** This means you can add numbers or terms in any order without changing the result.
Examples:
$$3 + 5 = 8 \quad \Rightarrow \quad 5 + 3 = 8$$
$$y + 5 = 5 + y$$
$$8 + y + 10 = 10 + y + 8$$
6. **Multiplication is commutative:** You can multiply numbers or terms in any order.
Examples:
$$5y = y5$$
$$5 \times 3 = 15$$
$$3 \times 5 = 15$$
7. **Summary:** To evaluate expressions, substitute values, perform multiplication and addition, and combine like terms carefully. Remember addition and multiplication can be done in any order.
Final answer for the example evaluation: $17$.
Algebra Basics D82Ce8
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