Skill: Evaluate algebraic expressions by substitution

To evaluate an algebraic expression by substitution, replace each variable with its given value. Then simplify using the order of operations:

1. Parentheses
2. Exponents
3. Multiplication and division
4. Addition and subtraction

Always use parentheses when substituting a negative number.

Example: Evaluate

$$2x^2+3(y-1)$$

when $x=-2$ and $y=\frac12$.

Step 1: Substitute the given values

Replace $x$ with $-2$ and $y$ with $\frac12$:

$$2(-2)^2+3\left(\frac12-1\right)$$

The parentheses around $-2$ are important because the negative number is being squared.

Step 2: Simplify the parentheses and exponent

$$(-2)^2=4$$

and

$$\frac12-1=-\frac12$$

So the expression becomes

$$2(4)+3\left(-\frac12\right)$$

Step 3: Multiply

$$8-\frac32$$

Step 4: Subtract

Rewrite $8$ as $\frac{16}{2}$:

$$\frac{16}{2}-\frac{3}{2}=\frac{13}{2}$$

Therefore,

$$\boxed{\frac{13}{2}}$$

The value of the expression is $\frac{13}{2}$, or $6.5$.