For each expression, write an equivalent expression that uses only addition.

1. \(20-9+8-7\)
2. \(4x-7y-5z+6\)
3. \(\text-3x-8y-4-\frac87z\)

Use the distributive property to write an expression that is equivalent to each expression. If you get stuck, consider drawing boxes to help organize your work.

1. \(9(4x-3y-\frac23)\)
2. \(\text-2(\text-6x+3y-1)\)
3. \(\frac15(20y-4x-13)\)
4. \(8(\text-x-\frac12)\)
5. \(\text-8(\text-x-\frac34y+\frac72)\)

Here are two different patterns made out of the same five identical isosceles triangles. Without using a protractor, determine the measures of Angles \(x\) and \(y\). Explain or show your reasoning.

First diagram, a regular pentagon, segments from the center to eact vertex form 5 identical circles.  Each of the middle angles is colored blue and labeled x, the angles of the triangles around the perimeter are colored yellow and labeled y.  For the second diagram, the triangles from the first diagram have been rearranged so that the center is blue, yellow, yellow, x, yellow.  The 5 triangles do not rearrange to make a complete convex polygon, but the angles y, y, and x together form a straight angle.

Match each equation to a step that will help solve the equation for \(x\).

Here are five sums. Use the distributive property to write each sum as a product with two factors.

1. \(2a+7a\)
2. \(5z-10\)
3. \(c-2cd\)
4. \(r+r+r+r\)
5. \(2x-\frac12\)