# Lesson 1

Inputs and Outputs

Let’s make some rules.

### Problem 1

Given the rule:

input | 0 | 2 | 4 | 6 | 8 | 10 |
---|---|---|---|---|---|---|

output |

### Problem 2

Here is an input-output rule:

input | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
---|---|---|---|---|---|---|---|

output |

### Problem 3

Andre’s school orders some new supplies for the chemistry lab. The online store shows a pack of 10 test tubes costs $4 less than a set of nested beakers. In order to fully equip the lab, the school orders 12 sets of beakers and 8 packs of test tubes.

- Write an equation that shows the cost of a pack of test tubes, \(t\), in terms of the cost of a set of beakers, \(b\).
- The school office receives a bill for the supplies in the amount of $348. Write an equation with \(t\) and \(b\) that describes this situation.
- Since \(t\) is in terms of \(b\) from the first equation, this expression can be substituted into the second equation where \(t\) appears. Write an equation that shows this substitution.
- Solve the equation for \(b\).
- How much did the school pay for a set of beakers? For a pack of test tubes?

### Problem 4

Solve: \(\begin{cases} y=x-4 \\ y=6x-10\\ \end{cases}\)

### Problem 5

For what value of \(x\) do the expressions \(2x+3\) and \(3x-6\) have the same value?