Explain how the parts of the balanced hanger diagram compare to the parts of the equation.

\(7=2x+3\)

For the hanger diagram shown:

1. Write an equation with the variable \(x\) to represent the relationship.
2. Draw more hanger diagrams or describe how you would change the given diagram to show each step you would take to find the value of \(x\). Explain your reasoning.
3. Write an equation to represent each hanger diagram you drew or each change you would make to the given diagram. Explain how each equation matches its diagram.

Match each story to an equation.

In each equation, the ? represents an operation. Which operation makes each equation true?

1.  \(48 \text{ ? } (\text-8) = (\text-6)\)
2. \((\text-40) \text{ ? } 8 = (\text-5)\)
3. \(12 \text{ ? } (\text-2) = 14\)
4. \(18 \text{ ? } (\text-12) = 6\)
5. \(18 \text{ ? } (\text-20) = \text-2\)
6. \(22 \text{ ? } (\text-0.5) = \text-11\)

Describe a sequence of rotations, reflections, translations, and dilations that show one figure is similar to the other. Be sure to include the distance and direction of a translation, a line of reflection, the center and angle of a rotation, and the center and scale factor of a dilation.

polar coordinate plane with center at A. quadrilateral BCDE and QRST graphed. B at 9 comma pi over 12. C at 6 comma pi over 4. D at 3 comma 5 pi over 12, E at 6 comma 11 pi over 6. Q at 3 comma 5 pi over 3. R at 2 comma 11 pi over 6. S at 1 comma 0 pi. T at 2 comma 17 pi over 12.