1. Let's start with basic arithmetic operations involving positive and negative numbers. For example, consider the expression $-3 + 7 - 2$.
2. We perform the operations from left to right: first $-3 + 7 = 4$, then $4 - 2 = 2$. So, the result is $2$.
3. Now, let's move to algebraic expressions with variables like $a$, $b$, and $x$. Suppose we have the expression $3a - 2b + 4x$.
4. To simplify or evaluate such expressions, we need values for $a$, $b$, and $x$. For example, if $a=2$, $b=1$, and $x=3$, then substitute these values:
$$3(2) - 2(1) + 4(3) = 6 - 2 + 12 = 16$$
5. When simplifying algebraic expressions, remember to combine like terms (terms with the same variable and exponent) and apply arithmetic operations carefully.
6. For example, simplify $5a + 3b - 2a + 4b$:
$$5a - 2a + 3b + 4b = (5 - 2)a + (3 + 4)b = 3a + 7b$$
7. Always keep track of positive and negative signs, and use parentheses to clarify operations when needed.
This covers basic arithmetic with positive and negative numbers and algebraic expressions with variables.
Basic Arithmetic Algebra Dae103
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