Lesson 20
Combining Like Terms (Part 1)
Problem 1
Andre says that \(10x+6\) and \(5x+11\) are equivalent because they both equal 16 when \(x\) is 1. Do you agree with Andre? Explain your reasoning.
Problem 2
Select all expressions that can be subtracted from \(9x\) to result in the expression \(3x+5\).
$\text-5+6x$
$5-6x$
$6x+5$
$6x-5$
$\text-6x+5$
Problem 3
Select all the statements that are true for any value of \(x\).
$7x + (2x+7) = 9x+7$
$7x + (2x - 1) = 9x + 1$
$\frac12 x+(3 - \frac12 x)=3$
$5x - (8 - 6x) =\text-x-8$
$0.4x - (0.2x+8) =0.2x-8$
$6x - (2x -4)=4x+4$
Problem 4
For each situation, would you describe it with \(x< 25\), \(x > 25\), \(x \leq 25\), or \(x \geq 25\)?
- The library is having a party for any student who read at least 25 books over the summer. Priya read \(x\) books and was invited to the party.
- Kiran read \(x\) books over the summer but was not invited to the party.
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Problem 5
Consider the problem: A water bucket is being filled with water from a water faucet at a constant rate. When will the bucket be full? What information would you need to be able to solve the problem?