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Introduction to :

Remember that a variable is like an empty box that is waiting for a number. It is a box, and it waits patiently. 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 Problems

1. Substitute 3 for x in the expression 4x + 5. 4x + 5 is the same as 4 · ☐ + 5, so write 3 in the box: 4 · [ 3 ] + 5.

To substitute a value for a variable, replace every copy of the variable with the value enclosed in parentheses.

2. Substitute 4 for y in the expression 2yy2. Replace every occurrence of y with (4); 2(4) + (4)2. 4ou see? What did 4ou say? We can stop now? Oh. Thank 4ou.

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

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?

Sample Problem

If we forget the parentheses when substituting - 4 for y in the expression 2y + y2, we find that 2 - 4 + - 42. This step gives us - 2 - 16 = - 18, which is completely wrong! Not just a little wrong, which would be bad enough, but completely wrong!

Example 1

Evaluate the expression 4x + 5 for x = 3.


Example 2

Evaluate the expression 2y + y2 if y = 4.


Example 3

If y = - 4, evaluate the expression 2y + y2.


Exercise 1

Evaluate 3x + 4 for x = - 2

Exercise 2

Evaluate  for x = 10.

Exercise 3

Evaluate 4x2 for x = - 1.

Exercise 4

Evaluate 5y - 3y2 for y = - 2.

Exercise 5

Evaluate z3 - 18 + z for z = - 2.

Exercise 6

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

Exercise 7

Evaluate b2 - 4ac for a = 1, b = 3 and c = - 2.

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