# At a Glance - Evaluating Expressions by Substitution

Remember that a variable is like an empty box that's waiting for a number. Have you ever seen a box wait? Those things have unbelievable staying power.

We call it **substitution** when we put a number into the box.

### Sample Problem

What's the value of 4*x* + 5 when *x* = 3?

Let's break it down: 4*x* + 5 is the same as 4 · ☐ + 5, so write 3 in the box:

4(3) + 5

After substituting values for the variables in an expression, we can **evaluate** the expression by working out the arithmetic.

4(3) + 5 =

12 + 5 = 17

Long story short: to substitute a value for a variable, replace every copy of the variable with the value enclosed in parentheses.

### Sample Problem

What's the value of 2*y* + *y*^{2} when *y* = 4?

Here we go: replace every occurrence of *y* with 4:

2(4) + (4)^{2}

4ou see? What did 4ou say? We can stop now? Oh. Thank 4ou.

2(4) + (4)^{2} =

8 + 16 = 24

**Be Careful:** Make sure to put parentheses around values when substituting for variables. There can be some mix-ups with negative signs otherwise. We don't want no more mix-ups. Not after that failed bank heist. You hear that, Ira?

#### Example 1

What's the value of the expression 5 |

#### Example 2

What's the value of 3 |

#### Example 3

If |

#### Exercise 1

Evaluate -3*x* + 4 for *x* = -2.

#### Exercise 2

Evaluate for *x* = 10.

#### Exercise 3

Evaluate 4*x*^{2} for *x* = -1.

#### Exercise 4

Evaluate 5*y* – 3*y*^{2} for *y *= -2.

#### Exercise 5

Evaluate *z*^{3 }– 18 + *z* for *z* = -2.

#### Exercise 6

Evaluate 4*xyz* + *x* + *y* – *z* for *x* = 2, *y* = 3, and *z* = 5.

#### Exercise 7

Evaluate *b*^{2} – 4*ac* for *a* = 1, *b* = 3 and *c* = -2.