35 Midterm 1: Version E

1. Simplify the following:
   1. \(-(3)^2\)
   2. \((- 3)^2\)
   3. \(- 3^2\)
   4. \(3 ( 2 + 4 ) - ( 2 \cdot 4 ) \)
   5. \(- | -5 + 8|\)
2. Solve for \(x\) in the equation \(2(x - 4) + 18 = -12 + 4(x + 3).\)
3. Isolate the variable \(r_1\) in the equation \(\dfrac{1}{R}-\dfrac{1}{r_1} = \dfrac{1}{r_2}.\)
4. Solve for \(x\) in the equation \(\dfrac{x}{12} - \dfrac{x-4}{3}=\dfrac{2}{3}.\)
5. Find the equation of the horizontal line that passes through the point \((-4, -6).\)
6. Find the equation that has a slope of \(\dfrac{2}{5}\) and passes through the point \((-1, 1).\)
7. Find the equation of the line passing through the points \((0, -1)\) and \((2, 5).\)
8. Graph the relation \(y=\dfrac{2}{3}x + 1.\)

For questions 9 to 11, find each solution set and graph it.

9. \(-20 \le 8x - 4 \le 28\)
10. \(\left| \dfrac{2x+2}{6} \right| \le 2\)
11. \(\left| \dfrac{3x-4}{5}\right| >1\)
12. Graph \(3x - 2y < 12.\)
13. Find three consecutive odd integers such that the sum of the first integer, two times the second integer, and three times the third integer is 94.
14. Karl is going to cut a 800 cm cable into 2 pieces. If the first piece is to be 3 times as long as the second piece, find the length of each piece.
15. \(y\) varies jointly with \(m\) and inversely with the square of \(n.\) If \(y = 12\) when \(m = 3\) and \(n = 4,\) find the constant \(k,\) then use \(k\) to find \(y\) when \(m = 3\) and \(n = -3.\)

Midterm 1: Version E Answer Key