Section 4.1: Unit 0 Practice Answers

MTH 65: Algebra 2 · LibreTexts

0%

Contents

    Text

    Size
    100%
    Theme
    Typeface
    Line length
    Spacing

    From LibreTexts, under CC BY-NC 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Unit 0 Answers

    Section 0.1P: Order of Operations

    1. 125
    2. 256
    3. 43
    4. 55
    5. 5
    6. 34
    7. 58
    8. 6
    9. 4
    10. 35
    11. 58
    12. 149
    13. 50

    Section 0.2P: Fractions

    1. \(-\dfrac{12}{7}\)
    2. \(\dfrac{10}{21}\)
    3. \(\dfrac{2x^2}{3y}\)
    4. \(-\dfrac{21a^2}{11b^2}\)
    5. \(\dfrac{1}{3}\)
    6. \(-\dfrac{21}{50}\)
    7. \(9n\)
    8. \(-\dfrac{4}{9}\)
    9. \(-\dfrac{10}{9}\)
    10. \(\dfrac{2m}{3n}\)
    11. \(\dfrac{29}{24}\)
    12. \(\dfrac{1}{48}\)
    13. \(\dfrac{1}{12}\)
    14. \(\dfrac{4x+3}{12}\)
    15. \(-\dfrac{5(a+1)}{3}\)
    16. \(a\)
    17. \(\dfrac{9}{7}\)
    18. \(\dfrac{11}{6}\)
    19. \(\dfrac{15}{4}\)
    20. \(\dfrac{5}{21}\)
    21. \(\dfrac{5}{4}\)
    22. \(\dfrac{1}{24}\)
    23. \(\dfrac{33}{64}\)
    24. \(\dfrac{7}{9}\)
    25. \(-5\)
    26. \(\dfrac{11}{5}\)
    27. \(1\)
    28. \(\dfrac{13}{3}\)
    29. Answers will vary
    30. Answers will vary

    Section 0.3P: General Strategy to Solve Linear Equations

      1. \(\text{yes}\)
      2. \(\text{no}\)
      1. \(\text{no}\)
      2. \(\text{yes}\)
    3. \(y=5\)
    4. \(w=-18\)
    5. \(q=3\)
    6. \(c=4\)
    7. \(y=-5\)
    8. \(p=-4\)
    9. \(c=-4\)
    10. \(m=6\)
    11. \(x=-1\)
    12. \(a=\dfrac{3}{4}\)
    13. \(w=\dfrac{9}{4}\)
    14. \(p=-41\)
    15. \(n=-3\)
    16. \(u=3\)
    17. \(x=18\)
    18. \(n=9\)
    19. \(d=8\)
    20. identity; all real numbers
    21. conditional equation; \(j=\dfrac{2}{5}\)
    22. contradiction; no solution
    23. identity; all real numbers
    24. The length is \(19.75\) feet
    25. Answers will vary
    26. Answers will vary

    Section 0.4P: General Strategy to Solve Linear Inequalities

    1. Number line graph of x > 3. Interval notation: (3, ∞)
    2. Number line graph of x ≤ -0.5. Interval notation: (-∞, -0.5]
    3. Number line graph of x ≥ 1/3. Interval notation: [1/3, ∞)
    4. Number line graph of x ≤ 5. Interval notation: (-∞, 5]
    5. Number line graph of x ≥ -1.5. Interval notation: [-1.5, ∞)
    6. Solution shown: m ≤ 107; number line with bracket at 107 and shading left; interval (-∞, 107]
    7. Solution shown: v > −9; number line with parenthesis at −9 and shading right; interval (−9, ∞)
    8. Solution shown: b ≥ −17/24; number line with bracket at −17/24 and shading right; interval [−17/24, ∞)
    9. Solution shown: g < 23/36; number line with parenthesis at 23/36 and shading left; interval (−∞, 23/36)
    10. Solution shown: s ≥ 9; number line with bracket at 9 and shading right; interval [9, ∞)
    11. Solution shown: v ≥ −12; number line with bracket at −12 and shading right; interval [−12, ∞)
    12. Solution shown: k > 64; number line with parenthesis at 64 and shading right; interval (64, ∞)
    13. Solution shown: g ≤ 16; number line with bracket at 16 and shading left; interval (−∞, 16]
    14. Solution shown: p < 18/5; number line with parenthesis at 18/5 and shading left; interval (−∞, 18/5)
    15. Solution shown: y < −5; number line with parenthesis at −5 and shading left; interval (−∞, −5)
    16. Solution shown: x ≤ 7; number line with bracket at 7 and shading left; interval (−∞, 7]
    17. Identity: all real numbers; number line fully shaded both directions; interval (−∞, ∞)
    18. Contradiction: no solution; blank number line; text: No solution
    19. Contradiction: no solution; blank number line; text: No solution
    20. Contradiction: no solution; blank number line; text: No solution
    21. Solution shown: k ≥ −11/5; number line with bracket at −11/5 and shading right; interval [−11/5, ∞)
    22. Contradiction: no solution; blank number line; text: No solution
    23. Solution shown: y ≥ 10/49; number line with bracket at 10/49 and shading right; interval [10/49, ∞)
    24. Solution shown: d > −90; number line with parenthesis at −90 and shading right; interval (−90, ∞)
    25. Solution shown: n ≤ −78; number line with bracket at −78 and shading left; interval (−∞, −78]
    26. Translated inequality: k + 6 > 25; Solution: k > 19; interval (19, ∞); graphed with parenthesis at 19, shading right
    27. Translated inequality: x − 12 ≥ 21; Solution: x ≥ 33; interval [33, ∞); graphed with bracket at 33, shading right
    28. Translated inequality: −2s < 56; Solution: s > −28; interval (−28, ∞); graphed with parenthesis at −28, shading right
    29. up to 12 people
    30. up to 5 drinks
    31. 31 aprons or more
    32. more than $15,000 in sales
    33. 44 meals or more
    34. 49 cars or more
    35. up to 91 students
    36. 169 or fewer guests
    37. Answers will vary.

    Section 0.5P: Solving Systems of Linear Equations

      1. yes
      2. no
      1. yes
      2. no
    3. Graph showing lines intersecting at the point (1, 2).Solution Point: \((1,2)\)
    4. Graph showing the two lines intersecting at the point (6, -2). Solution Point: \((6,−2)\)
    5. Graph showing the two lines intersecting at the point (-3, 1). Solution Point: \((−3,1)\)
    6. Graph showing two parallel lines no solution
    7. Both equations represent the same line, so all points on the line are solutions of the system. infinitely many solutions with solution set: \(\big\{ (x,y) | 2 x+y=6\big\}\)
    8. \((0,2)\)
    9. \((2,4)\)
    10. \((1,2)\)
    11. \((3,2)\)
    12. \((1,1)\)
    13. \((-2,-2)\)
    14. \((3,3)\)
    15. infinitely many solutions: \(\{(x,y)\mid y=-\tfrac{1}{3}x+\tfrac{4}{3}\}\)
    16. infinitely many solutions: \(\{(x,y)\mid y=-\tfrac{1}{3}x-2\}\)
    17. \((2,2)\)
    18. no solution
    19. \(\left(\tfrac{1}{2},4\right)\)
    20. infinitely many solutions: \(\{(x,y)\mid y=-\tfrac{1}{2}x+5\}\)
    21. infinitely many solutions: \(\{(x,y)\mid y=2x+3\}\)
    22. Molly needs 16 ounces of strawberry juice and 48 ounces of water.
    23. Enrique needs 8 ounces of nuts and 16 ounces of raisins.
    24. Leo should plant 50 tulip bulbs and 300 daffodil bulbs.
    25. Answers will vary

    This page titled Section 4.1: Unit 0 Practice Answers was last modified on Mon, 08 Dec 2025 22:44:07 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Math Department.