37 Practice: Linear Equations, Inequalities, & Geometric Word Problems (2.1 – 2.3; 4.1; 4.5) — Intermediate Algebra

Answer key in next section.

2.1 Solving Elementary Linear Equations

For questions 1 to 28, solve each linear equation.

  1. v + 9 = 16
  2. 14 = b + 3
  3. x - 11 = -16
  4. -14 = x - 18
  5. 30 = a + 20
  6. -1 + k = 5
  7. x - 7 = -26
  8. -13 + p = -19
  9. 13 = n - 5
  10. 22 = 16 + m
  11. 340 = -17x
  12. 4r = -28
  13. {-9} = \dfrac{n}{12}
  14. 27 = 9b
  15. 20v = -160
  16. -20x = -80
  17. 340 = 20n
  18. 12 = 8a
  19. 16x = 320
  20. 8k = -16
  21. -16 + n = -13
  22. -21 = x - 5
  23. p-8 = -21
  24. m - 4 = -13
  25. \dfrac{r}{14} = \dfrac{5}{14}
  26. \dfrac{n}{8} = {40}
  27. 20b = -200
  28. -\dfrac{1}{3} = \dfrac{x}{12}

2.2 Solving Linear Equations

For questions 1 to 20, solve each linear equation.

  1. 5 + \dfrac{n}{4} = 4
  2. -2 = -2m + 12
  3. 102 = -7r + 4
  4. 27 = 21 - 3x
  5. -8n + 3 = -77
  6. -4 - b = 8
  7. 0 = -6v
  8. -2 + \dfrac{x}{2} = 4
  9. -8 = \dfrac{x}{5} - 6
  10. -5 = \dfrac{a}{4} - 1
  11.  0 = -7 + \dfrac{k}{2}
  12. -6 = 15 + 3p
  13. -12 + 3x = 0
  14. -5m + 2 = 27
  15. \dfrac{b}{3} + 7 = 10
  16. \dfrac{x}{1} - 8 = -8
  17. 152 = 8n + 64
  18. -11 = -8 + \dfrac{v}{2}
  19. -16 = 8a + 64
  20. -2x - 3 = -29

2.3 Solving Intermediate Linear Equations

For questions 1 to 26, solve each linear equation.

  1. 2 - (-3a - 8) = 1
  2. 2(-3n + 8) = -20
  3. -5(-4 + 2v) = -50
  4. 2 - 8(-4 + 3x) = 34
  5. 66 = 6(6 + 5x)
  6. 32 = 2 - 5(-4n + 6)
  7. -2 + 2(8x -9) = -16
  8. -(3 - 5n) = 12
  9. -1 - 7m = -8m + 7
  10. 56p - 48 = 6p +2
  11. 1 - 12r = 29 - 8r
  12. 4 + 3x = -12x + 4
  13. 20 - 7b = -12b + 30
  14. -16n + 12 = 39 - 7n
  15. -2 - 5(2 - 4m) = 33 + 5m
  16. -25 - 7x = 6(2x - 1)
  17. -4n + 11 = 2(1 - 8n) + 3n
  18. -7(1 + b) = -5 - 5b
  19. -6v-29 = -4v - 5(v+1)
  20. -8(8r - 2) = 3r + 16
  21. 2(4x - 4) = -20 - 4x
  22. -8n - 19 = -2(8n - 3) + 3n
  23. -2(m - 2) + 7(m - 8) = -67
  24. 7 = 4(n - 7) + 5(7n + 7)
  25. 50 = 8(7 + 7r) - (4r + 6)
  26. -8(6 + 6x) + 4(-3 + 6x) = -12

4.1 Solving Linear Inequalities

For questions 1 to 6, draw a graph for each inequality and give its interval notation.

  1. n  > -5
  2. n  >  4
  3. -2 \le k
  4. 1 \ge k
  5. 5 \ge x
  6. -5 < x

For questions 7 to 12, write the inequality represented on each number line and give its interval notation.

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For questions 13 to 38, draw a graph for each inequality and give its interval notation.

  1. \dfrac{x}{11}\ge 10
  2. -2 \le \dfrac{n}{13}
  3. 2 + r < 3
  4. \dfrac{m}{5} \le -\dfrac{6}{5}
  5. 8+\dfrac{n}{3}\ge 6
  6. 11 > 8+\dfrac{x}{2}
  7. 2 > \dfrac{(a-2)}{5}
  8. \dfrac{(v-9)}{-4} \le 2
  9. -47 \ge 8 -5x
  10. \dfrac{(6+x)}{12} \le -1
  11. -2(3+k) < -44
  12. -7n-10 \ge 60
  13. 18 < -2(-8+p)
  14. 5 \ge \dfrac{x}{5} + 1
  15. 24 \ge -6(m - 6)
  16. -8(n - 5) \ge 0
  17. -r -5(r - 6) < -18
  18. -60 \ge -4( -6x - 3)
  19. 24 + 4b < 4(1 + 6b)
  20. -8(2 - 2n) \ge -16 + n
  21. -5v - 5 < -5(4v + 1)
  22. -36 + 6x > -8(x + 2) + 4x
  23. 4 + 2(a + 5) < -2( -a - 4)
  24. 3(n + 3) + 7(8 - 8n) < 5n + 5 + 2
  25. -(k - 2) > -k - 20
  26. -(4 - 5p) + 3 \ge -2(8 - 5p)

4.5 Geometric Word Problems

For questions 1 to 8, write the formula defining each relation. Do not solve.

  1. The length of a rectangle is 3 cm less than double the width, and the perimeter is 54 cm.
  2. The length of a rectangle is 8 cm less than double its width, and the perimeter is 64 cm.
  3. The length of a rectangle is 4 cm more than double its width, and the perimeter is 32 cm.
  4. The first angle of a triangle is twice as large as the second and 10° larger than the third.
  5. The first angle of a triangle is half as large as the second and 20° larger than the third.
  6. The sum of the first and second angles of a triangle is half the amount of the third angle.
  7. A 140 cm cable is cut into two pieces. The first piece is five times as long as the second.
  8. A 48 m piece of hose is to be cut into two pieces such that the second piece is 5 m longer than the first.

For questions 9 to 18, write and solve the equation describing each relationship.

  1. The second angle of a triangle is the same size as the first angle. The third angle is 12° larger than the first angle. How large are the angles?
  2. Two angles of a triangle are the same size. The third angle is 12° smaller than the first angle. Find the measure of the angles.
  3. Two angles of a triangle are the same size. The third angle is three times as large as the first. How large are the angles?
  4. The second angle of a triangle is twice as large as the first. The measure of the third angle is 20° greater than the first. How large are the angles?
  5. Find the dimensions of a rectangle if the perimeter is 150 cm and the length is 15 cm greater than the width.
  6. If the perimeter of a rectangle is 304 cm and the length is 40 cm longer than the width, find the length and width.
  7. Find the length and width of a rectangular garden if the perimeter is 152 m and the width is 22 m less than the length.
  8. If the perimeter of a rectangle is 280 m and the width is 26 m less than the length, find its length and width.
  9. A lab technician cuts a 12 cm piece of tubing into two pieces such that one piece is two times longer than the other. How long are the pieces?
  10. An electrician cuts a 30 m piece of cable into two pieces. One piece is 2 m longer than the other. How long are the pieces?

 

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