Unit 4, Lesson 9
Strategic Solving
Accelerated 7
Practice
Problem 1
Solve each of these equations. Explain or show your reasoning.
\(2b+8-5b+3=\text-13+8b-5\)
\(2x+7-5x+8=3(5+6x)-12x\)
\(2c-3=2(6-c)+7c\)
Problem 2
Solve each equation and check your solution.
\(\text-3w-4=w+3\)
\(3(3-3x)=2(x+3)-30\)
\(\frac13(z+4)-6=\frac23(5-z)\)
Problem 3
Elena said the equation \(9x+15=3x+15\) has no solutions because \(9x\) is greater than \(3x\). Do you agree with Elena? Explain your reasoning.
Problem 4
Clare asks Andre to play the following number puzzle:
- Pick a number
- Add 2
- Multiply by 3
- Subtract 7
- Add your original number
Andre’s final result is 27.
Which number did he start with?
Problem 5
Label the arrows to describe each move.
Problem 6
Complete the equation with a number that makes the expression on the right side of the equal sign equivalent to the expression on the left side.
\(\displaystyle 5x-2.5 +6x-3 = \underline{\hspace{.5in}}(2x-1)\)