Solve the Inequality: (5x-8)/3 > 9

GeoGebra Commands & Parameters

1. LaTeX("\text{Eliminate the denominator.}") → step1
2. LaTeX("\text{ \textcolor{#000099}{>}}") → step3_1
3. LaTeX("\text{Original inequality }") → step3_3
4. LaTeX("\text{ \textcolor{#000099}{>}}") → step4_1
5. LaTeX("\text{ \textcolor{#000099}{>}}") → step5_2
6. LaTeX("\text{Simplify.}") → step5_4
7. LaTeX("\text{Isolate the term with the variable. }") → step7
8. LaTeX("\textcolor{#000099}{\text{>}}") → step9_2
9. LaTeX("\text{Inequality from the previous step}") → step9_4
10. LaTeX("\textcolor{#000099}{\text{>}}") → step10_2
11. LaTeX("\textcolor{#000099}{\text{>}}") → step11_2
12. LaTeX("\text{Simplify.}") → step11_4
13. LaTeX("\text{Isolate the variable. }") → step13
14. LaTeX("\textcolor{#000099}{>}") → step15_2
15. LaTeX("\text{Inequality from the previous step}") → step15_4
16. LaTeX("\textcolor{#000099}{>}") → step16_2
17. LaTeX("\textcolor{#000099}{>}") → step17_3
18. LaTeX("\textcolor{#000099}{\text{x}}") → step17_1
19. LaTeX("\text{Simplify.}") → step17_4
20. LaTeX("\text{Check the result. }") → step19
21. LaTeX("\text{\textcolor{#000099}{>}}") → step21_2
22. LaTeX("\text{Original inequality}") → step21_4
23. LaTeX("\text{\textcolor{#000099}{>}}") → step22_2
24. LaTeX("\text{\textcolor{#000099}{>}}") → step23_2
25. LaTeX("\text{Multiply.}") → step23_4
26. LaTeX("\text{\textcolor{#000099}{>}}") → step24_2
27. LaTeX("\text{Subtract.}") → step24_4
28. LaTeX("\text{\textcolor{#000099}{>}}") → step25_2
29. LaTeX("\text{Divide.}") → step25_3
30. LaTeX((((((("\text{ \textcolor{#000099}{\frac{" * Value1) * "x-") * Value2) * "}{") * Value3) * "}}}")) → step3
31. LaTeX((((("\text{ \textcolor{#000099}{" * Value1) * "x-") * Value2) * "}}")) → step5_1
32. LaTeX((("\textcolor{#000099}{\text{" * mul) * "}}")) → step5_3
33. LaTeX((("\text{Perform the inverse operation of adding \textcolor{#000099}{" * Value2) * "} to both sides of the inequality. }")) → step8
34. LaTeX((("\textcolor{#000099}{\text{" * mul) * "}}")) → step9_3
35. LaTeX((("\textcolor{#000099}{\text{" * Value1) * "x}}")) → step11_1
36. LaTeX((("\textcolor{#000099}{\text{" * add) * "}}")) → step11_3
37. LaTeX((((("\text{The inequality is equivalent to \textcolor{#000099}{" * Value1) * "x > ") * add) * "}.}")) → step12
38. LaTeX((("\text{\textcolor{#000099}{" * add) * "}}")) → step15_3
39. LaTeX((((("\textcolor{#000099}{\text{\frac{" * Value1) * "x}{") * Value1) * "}}}")) → step16_1
40. LaTeX((("\text{Divide both sides by \textcolor{#000099}{" * Value1) * "}.}")) → step16_4
41. LaTeX((((("\text{\textcolor{#000099}{\frac{" * add) * "}{") * Value1) * "}}}")) → step16_3
42. LaTeX((("\text{\textcolor{#000099}{" * div) * "}}")) → step17_2
43. LaTeX((((((("\text{\textcolor{#000099}{\frac{" * Value1) * "x-") * Value2) * "}{") * Value3) * "}}}")) → step21_1
44. LaTeX((((((("\text{\textcolor{#000099}{\frac{" * sum) * "-") * Value2) * "}{") * Value3) * "}}}")) → step23_1
45. LaTeX((((("\text{\textcolor{#000099}{\frac{" * final) * "}{") * Value3) * "}}}")) → step24_1
46. LaTeX((("\text{\textcolor{#000099}{" * result) * "}}")) → step25_1
47. LaTeX((("\text{\textcolor{#000099}{x > " * div) * "} is correct.}")) → step27
48. LaTeX((("\text{Add \textcolor{#000099}{" * Value2) * "} to both sides.}")) → step10_4
49. LaTeX((("\textcolor{#000099}{\text{" * Value1) * "x}}")) → step15_1
50. LaTeX((("\text{Multiply both sides of the inequality by \textcolor{#000099}{" * Value3) * "}.}")) → step4_6
51. LaTeX((((((("\textcolor{#000099}{\text{" * Value1) * "x \textendash ") * Value2) * "+") * Value2) * "}}")) → step10_1
52. LaTeX((((((((("\text{\textcolor{#000099}{\frac{" * Value1) * "(") * check) * ")-") * Value2) * "}{") * Value3) * "}}}")) → step22_1
53. LaTeX((((((((("\text{Solve the inequality \textcolor{#000099}{\frac{" * Value1) * "x-") * Value2) * "}{") * Value3) * "}>") * var4) * ".}}")) → Mainquestion
54. LaTeX(((" \textcolor{#000099}{\text{" * var4) * "}}")) → step3_2
55. LaTeX((((((((((((((("\text{The inequality \textcolor{#000099}{\frac{" * Value1) * "x-") * Value2) * "}{") * Value3) * "}>") * var4) * "} is equivalent to \textcolor{#000099}{") * Value1) * "x-") * Value2) * ">") * mul) * "}.}")) → step6
56. LaTeX((("\text{\textcolor{#000099}{" * var4) * "}}")) → step21_3
57. LaTeX((("\text{\textcolor{#000099}{" * var4) * "}}")) → step22_3
58. LaTeX((("\text{\textcolor{#000099}{" * var4) * "}}")) → step23_3
59. LaTeX((("\text{\textcolor{#000099}{" * var4) * "}}")) → step24_3
60. LaTeX((("\text{\textcolor{#000099}{" * var4) * "}}")) → step25_4
61. LaTeX("\text{Constant term in}") → data2_1
62. LaTeX("\text{ the numerator}") → data2_2
63. LaTeX("\text{Constant term in}") → data3_1
64. LaTeX("\text{ the denominator}") → data3_2
65. LaTeX((((("\textcolor{#000099}{\text{" * Value1) * "x \textendash ") * Value2) * "}}")) → step9_1
66. LaTeX((("\text{Substitute \textcolor{#000099}{" * check) * "} for \textcolor{#000099}{x}.}")) → step22_4
67. LaTeX((((((((("\text{ \textcolor{#000099}{\frac{" * Value1) * "x-") * Value2) * "}{") * Value3) * "}•") * Value3) * "}}")) → step4_2
68. LaTeX("\text{Coefficient of \textcolor{#000099}{x}}") → data1
69. LaTeX((((("\textcolor{#000099}{\text{" * var4) * "}•") * Value3) * "}")) → step4_3
70. LaTeX("\text{a rational function and the inequality is written in any of these forms:\textcolor{#000099}{f(x) < 0},}") → Wordstoknow_2
71. LaTeX((("\text{To eliminate the denominator, \textcolor{#000099}{" * Value3) * "}, perform the inverse operation of multiplication. (Recall that the denominator of a fraction}")) → step2
72. LaTeX("\text{represents division, which is the opposite of multiplication.)}") → step2_1
73. LaTeX((((("\textcolor{#000099}{\text{" * mul) * "+") * Value2) * "}}")) → step10_3
74. LaTeX((("\text{To isolate the variable, \textcolor{#000099}{x}, divide both sides of the inequality by the coefficient of \textcolor{#000099}{x}, which is \textcolor{#000099}{" * Value1) * "}.}")) → step14
75. LaTeX((((((((((("\text{The solution to the original inequality, \textcolor{#000099}{\frac{" * Value1) * "x-") * Value2) * "}{") * Value3) * "}>") * var4) * "}, is all numbers greater than \textcolor{#000099}{") * div) * "}.}")) → step18
76. LaTeX((((("\text{To check the solution \textcolor{#000099}{x > " * div) * "}, choose a number greater than \textcolor{#000099}{") * div) * "}, substitute it into the inequality, and solve to see if the result is a}")) → step20_1
77. LaTeX((("\text{true statement. Let’s try \textcolor{#000099}{" * check) * "}. Be sure to substitute this value into the original inequality.}")) → step20_2
78. LaTeX((((((("\text{\textcolor{#000099}{" * result) * " > ") * var4) * "} is a true statement. Therefore, any number greater than \textcolor{#000099}{") * div) * "} will result in a true statement, and the solution}")) → step26
79. LaTeX("\text{\mathbf{inequality} an \textcolor{#000099}{x}-value that makes \textcolor{#000099}{f(x)} = 0 or makes \textcolor{#000099}{f(x)} undefined, where \textcolor{#000099}{f(x)} is") → Wordstoknow_1
80. LaTeX("\text{\textcolor{#000099}{f(x) ≤ 0, \;f(x) > 0, \;or\;f(x) ≥ 0}}") → Wordstoknow_3