Unit 6, Lesson 21
Combining Like Terms (Part 2)
Grade 7
Practice
Problem 1
- Noah says that \(9x - 2x + 4x\) is equivalent to \(3x\), because the subtraction sign tells us to subtract everything that comes after \(9x\).
- Elena says that \(9x - 2x + 4x\) is equivalent to \(11x\), because the subtraction only applies to \(2x\).
Do you agree with either of them? Explain your reasoning.
Problem 2
Identify the error in generating an expression equivalent to \(4+2x-\frac12(10-4x)\). Then correct the error.
\(4+2x + \frac {\text{-}1}{2}(10 + \text-4x)\)
\(4+2x +\text-5 +2x\)
\(4+2x-5+2x\)
\(\text-1\)
Problem 3
Select all expressions that are equivalent to \(5x -15 - 20x+10\).
\(5x - (15+20x) + 10\)
\(5x+\text-15+\text-20x+10\)
\(5(x-3-4x+2)\)
\(\text-5(\text-x +3+4x+\text-2)\)
\(\text-15x-5\)
\(\text-5(3x+1)\)
\(\text-15(x - \frac13)\)
The school marching band has a budget of up to \$750 to pay for 15 new uniforms and competition fees that total \$300. How much can they spend on each uniform?
- Write an inequality to represent this situation.
- Solve the inequality and describe what it means in the situation.
Problem 5
Solve the inequality that represents each story. Then interpret what the solution means in the story.
- Each time Elena earns \$9, she gives \(x\) dollars to charity. Elena believes this will happen 7 times this month. She wants to be sure she keeps at least \$42 from this month’s earnings. \(7(9-x) \geq 42\)
- Lin buys a candle that is 9 inches tall and burns down \(\frac37\) inch per minute. She wants to let the candle burn down until it is less than 6 inches tall. \(9 - \frac{3}{7}x < 6\)
Problem 6
A certain shade of light blue paint is made by mixing \(1\frac12\) quarts of blue paint with 5 quarts of white paint. If you need a total of 16.25 gallons of this shade of light blue paint, how much of each color should you mix? (1 gallon = 4 quarts)