Lesson 1

Given the rule:

Complete the table for the function rule for the following input values: 

Here is an input-output rule:

Complete the table for the input-output rule: 

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.

1. Write an equation that shows the cost of a pack of test tubes, \(t\), in terms of the cost of a set of beakers, \(b\).
2. 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.
3. 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.
4. Solve the equation for \(b\).
5. How much did the school pay for a set of beakers? For a pack of test tubes?

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

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