Practice the questions given in the worksheet on linear equation in one variable.
I. Solve the following equations and check the result:
1. 2x – 6 = 0
2. 7x – 2 = 8 - x
3. 8 – 2x = 5 – 4x
4. 4 + 3x = 2 – 2x
5. 2(x – 1) + 2(3x -1) = 0
6. 4(x-1) –(2x – 5) = 4
7. 2x – \(\frac{2}{3}\) = \(\frac{3}{4}\) – x
8. \(\frac{x}{2}\) – 2= 4 + \(\frac{1}{4}\)
9. \(\frac{x}{9}\) + \(\frac{x}{3}\) = \(\frac{1}{9}\)
10. 3x + 2(x+2) = 10 – (2x – 5)
11. 10(y – 4) – 2(y – 9) – 5(y + 4) = 0
12. \(\frac{2m+5}{3}\) = 3m - 5
13. 6(3x + 2) – 5(6x – 1) = 2(x – 8) – 5(7x – 6) + 8x
14. t – (2t +5) – (1- 2t) = (3 + 4t) – 2(t - 4)
15. \(\frac{2x}{3}\) = \(\frac{3x}{4}\) + \(\frac{7}{12}\)
16. \(\frac{3x-1}{5}\) - \(\frac{x}{15}\) =3
17. 2x – 3 = \(\frac{3}{10}\) x (5x – 10)
18. \(\frac{2y – 1}{3}\) - \(\frac{y - 2}{4}\) = 1
19. \(\frac{x-2}{9}\) + \(\frac{1}{3}\) = x - \(\frac{2x - 1}{3}\)
20. \(\frac{2x - 1}{3}\) - \(\frac{2x - 2}{5}\) = \(\frac{1}{3}\)
21. \(\frac{y + 7}{15}\) = 1 + \(\frac{3y - 2}{5}\)
22. \(\frac{2x - 18}{7}\) + \(\frac{x}{3}\) = 2
23. \(\frac{2x - 3}{5}\) + \(\frac{x + 3}{4}\) = \(\frac{4x + 1}{4}\)
24. \(\frac{21x - 3}{4}\) – (2x - \(\frac{1 - x}{2}\)) = x + \(\frac{5}{2}\)
25. \(\frac{x + 2}{6}\) – (\(\frac{11 - x}{3}\)- \(\frac{1}{4}\)) = \(\frac{3x - 4}{9}\)
26. \(\frac{9x + 7}{2}\) – (x - \(\frac{x - 2}{12}\) = 24
27. 0.5x +\(\frac{x}{3}\) = 0.25x + 6
28. 0.18(5x – 4) = 0.5x + 0.6
29. 2.4(3 – x) – 0.3(2x – 3) = 0
30. 0.5x – (0.6 – 0.2x) = 0.2 – 0.3x
31. \(\frac{x + 2}{x - 2}\) = \(\frac{7}{2}\)
32. \(\frac{2x + 5}{3x + 4}\) = 5.
II. Solve the following word problems:
1. Ten added to thrice a whole number gives 40. Find the number.
2. Four-fifths of a number is greater than three-fourths of a number by 8. Find the number.
3. The sum of two consecutive multiples of 4 is 60. Find the number.
Solutions:
I. 1. x = 3
2. x = 5/4
3. x = -3/2
4. x = -2/5
5. x = 1/2
6. x = 3/2
7. x = 17/36
8. x = 25/4
9. x = 1/4
10. x = 11/7
11. y = 14
12.m = 20/7
13. x = -3/13
14. t = -17
15. x = -7
16. x = 6
17. x = 0
18. y = 2
19. x = -1
20. x = 1
21. y = -1/4
22. x = 96/13
23. x = -2/7
24. x = 11/7
25. x = 113/6
26. x = 248/43
27. x = 72/7
28. x = 3.3
29. x = 2.1
30. x = 0.8
31. x = 18/5
32. x = -15/13
II. 1. x = 10
2. x = 160
3. 1^{st} number = 28
2^{nd} number = 32
9th Grade Math
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