Problems

  1. Solve for $y$. Simplify your answer as much as possible.

    $-3(7y-8)+5y=2(y+7)$

  2. Solve for $v$. Simplify your answer as much as possible.

    $\dfrac{7}{2}v-\dfrac{5}{3}=-2v+\dfrac{5}{3}$

  3. Kala is participating in a 5 day cross-country biking challenge. She biked for 47, 51, 46, and 50 miles on the first four days. How many miles does she need to bike on the last day so that her average (mean) is 48 miles per day?

  4. Solve for $y$. $2(y+1)+4y=3(2y-1)+8$

  5. Solve. $-6(w+1)+8w=2(w-3)$

  6. Solve the inequality for $u$. Simplify your answer as much as possible.

    $u+\dfrac{2}{5}\le -\dfrac{1}{4}$

  7. Solve the inequality for $v$. Simplify your answer as much as possible.

    $-8\gt 3v+7$

  8. Solve the inequality for $w$.

    $14-\dfrac{1}{4}w\le 19$

  9. Solve the compound inequality. Write the solution in interval notation.

    (a) $3x-6 \lt -9$  or  $2x-5 \gt 3$

    (b) $-3v\ge -12$  or  $4v-5 \le -1$

    (c) $4x-3 \gt -27$  and $3x+3\gt 6$

    (d)$4w+4\lt 20$ and $2w+2\le-4$

  10. Solve.

    (a). $2|4x-4|+7 = 47$

    (b). $|6u+3|+66=9$

  11. Solve. Write your answer in interval notation.

    (a).$|2v|-22\lt -13$

    (b). $7|y+6|-9 \le -51$

    (c). $|4y+6|+4\ge 18$

  12. Graph the line.

    $y+3x=-2$

  13. Graph the line (a) $x=-6$ and (b) $y =4$

  14. Find the $x$-intercept and $y$-intercept of the line. Write your answers as ordered pairs.

    $2x-7y=-8$

  15. Find the slope of the line passing through the points $(-2, -7)$ and $(3, 5)$.

  16. Find an equation for the line that passes through the points $(-1,-4)$ and $(5, 6)$.

  17. Consider the line $-4x+5y=9$.

    (a) Find the equation of the line that is parallel to this line and passes through the point $(7, -4)$

    (b). Find the equation of the line that is perpendicular to this line and passes through the point $(7, -4)$

  18. Suppose that the relation is defined as follows.

    $T=\{(7, 7), (6, c), (c, 6), (0, d)\}$

    Give the domain and the range of $T$.

  19. The functions $f$ and $g$ are defined as follows.

    $f(x)=-3x^2-2$ and $g(x)=4x+2$

    Find (a). $f(5)$ and (b). $g(-7)$.

  20. The graph of a function $f$ is shown below.

    (a) Find one value of $x$ for which $f(x)=-1$.

    (b) Find $f(0)$.

    graph

  21. The graph of the relation $H$ is shown below.

    graph

    Give the domain and range of $H$. Write your answers using set notation.

  22. The entire graph of the function $g$ is shown in the figure below.

    Write the domain and range of $g$ using interval notation.

    graph

  23. Graph the function $h(x)=-\dfrac{2}{5}x+2$

Answer key

  1. $y=\dfrac{5}{9}$

  2. $v=\dfrac{20}{33}$

  3. $46$ miles.

  4. No solution.

  5. All real numbers are solutions.

  6. $u\le -\dfrac{13}{20}$

  7. $v\lt -5$

  8. $w \ge -20$

  9. (a). $(-\infty, -1) \cup (4, \infty)$

    (b). $(-\infty, 4]$

    (c). $(1, \infty)$

    (d). $(-\infty, -3]$

  10. (a). $x=6, -4$

    (b). no solution.

  11. (a). $\left(-\dfrac{9}{2}, \dfrac{9}{2}\right)$

    (b). no solution.

    (c). $(-\infty,-5]\cup[2,\infty)$

  12. Graph

  13. Graph

  14. $x$-intercept: $(-4,0)$; $y$-intercept:$(0,\dfrac{8}{7})$

  15. $\dfrac{12}{5}$

  16. $y+4=\dfrac{5}{3}(x+1)$

  17. (a). $y+4=\dfrac{4}{5}(x-7)$

    (b). $y+4=-\dfrac{5}{4}(x-7)$

  18. domain$=\{7, 6, c, 0\}$

    range$=\{7, c, 6, d\}$

  19. (a) $f(5)=-77$

    (b) $g(-7)=-26$

  20. (a) $-2$

    (b) $f(0)=3$

  21. domain $=\{-3, 3, -1, -4\}$

    range $=\{-3, -4, 2, 0\}$

  22. domain$=[-3, 3)$

    range$=[-4, 5]$

  23. graph