# 0.7e: Exercises - Linear Equations

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### A: Check a Solution

Exercise $$\PageIndex{1}$$

$$\bigstar$$ Determine whether or not the given value is a solution.

 $$−5x + 4 = −1 ; x = −1$$ $$4x − 3 = −7 ; x = −1$$ $$3y − 4 = 5; y = \frac{9}{3}$$ $$−2y + 7 = 12 ; y = −\frac{5}{2}$$ $$3a − 6 = 18 − a; a = −3$$ $$5 (2t − 1) = 2 − t; t = 2$$ $$ax − b = 0; x = \dfrac{b}{a}$$ $$ax + b = 2b; x = \dfrac{b}{a}$$

1. No $$\qquad$$ 3. Yes  $$\qquad$$ 5. No $$\qquad$$ 7. Yes

### B: Solve Linear Equations (I)

Exercise $$\PageIndex{2}$$

$$\bigstar$$ Solve.

 $$5x − 3 = 27$$ $$6x − 7 = 47$$ $$4x + 13 = 35$$ $$6x − 9 = 18$$ $$9a + 10 = 10$$ $$5 − 3a = 5$$ $$−8t + 5 = 15$$ $$−9t + 12 = 33$$ $$\dfrac{2}{3} x + \dfrac{1}{2} = 1$$ $$\dfrac{3}{8} x + \dfrac{5}{4} = \dfrac{3}{2}$$ $$\dfrac{1 − 3y}{5} = 2$$ $$\dfrac{2 − 5y}{6} = −8$$ $$7 − y = 22$$ $$6 − y = 12$$ Solve for $$x: ax − b = c$$ Solve for $$x: ax + b = 0$$

11. $$6$$ $$\qquad$$ 13. $$\frac{11}{2}$$ $$\qquad$$ 15. $$0$$ $$\qquad$$ 17. $$−\frac{5}{4}$$ $$\qquad$$ 19. $$\frac{3}{4}$$ $$\qquad$$ 21. $$−3$$ $$\qquad$$ 23. $$−15$$ $$\qquad$$ 25. $$x = \frac{b+c}{a}$$

### C: Solve Linear Equations (II)

Exercise $$\PageIndex{3}$$

$$\bigstar$$ Solve.

 $$6x − 5 + 2x = 19$$ $$7 − 2x + 9 = 24$$ $$12x − 2 − 9x = 5x + 8$$ $$16 − 3x − 22 = 8 − 4x$$ $$5y − 6 − 9y = 3 − 2y + 8$$ $$7 − 9y + 12 = 3y + 11 − 11y$$ $$3 + 3a − 11 = 5a − 8 − 2a$$ $$2 − 3a = 5a + 7 − 8a$$ $$\dfrac{1}{3} x −\dfrac{3}{2} + \dfrac{5}{2} x = \dfrac{5}{6} x + \dfrac{1}{4}$$ $$\dfrac{5}{8} + \dfrac{1}{5} x −\dfrac{3}{4} = \dfrac{3}{10} x − \dfrac{1}{4}$$ $$1.2x − 0.5 − 2.6x = 2 − 2.4x$$ $$1.59 − 3.87x = 3.48 − 4.1x − 0.51$$ $$5 − 10x = 2x + 8 − 12x$$ $$8x − 3 − 3x = 5x − 3$$ $$5 (y + 2) = 3 (2y − 1) + 10$$ $$7 (y − 3) = 4 (2y + 1) − 21$$ $$7 − 5 (3t − 9) = 22$$ $$10 − 5 (3t + 7) = 20$$ $$5 − 2x = 4 − 2 (x − 4)$$ $$2 (4x − 5) + 7x = 5 (3x − 2)$$ $$4 (4a − 1) = 5 (a − 3) + 2 (a − 2)$$ $$6 (2b − 1) + 24b = 8 (3b − 1)$$ $$\dfrac{2}{3} (x + 18) + 2 = \dfrac{1}{3} x − 13$$ $$\dfrac{2}{5} x − \dfrac{1}{2} (6x − 3) = \dfrac{4}{3}$$ $$1.2 (2x + 1) + 0.6x = 4x$$ $$6 + 0.5 (7x − 5) = 2.5x + 0.3$$ $$5 (y + 3) = 15 (y + 1) − 10y$$ $$3 (4 − y) − 2 (y + 7) = −5y$$ $$\dfrac{1}{5} (2a + 3) −\dfrac{1}{2} = \dfrac{1}{3} a + \dfrac{1}{10}$$ $$\dfrac{3}{2} a = \dfrac{3}{4} (1 + 2a) −\dfrac{1}{5} (a + 5)$$ $$6 − 3 (7x + 1) = 7 (4 − 3x)$$ $$6 (x − 6) − 3 (2x − 9) = −9$$ $$\dfrac{3}{4} (y − 2) + \dfrac{2}{3} (2y + 3) = 3$$ $$\dfrac{5}{4} − \dfrac{1}{2} (4y − 3) = \dfrac{2}{5} (y − 1)$$ $$−2 (3x + 1) − (x − 3) = −7x + 1$$ $$6 (2x + 1) − (10x + 9) = 0$$

31. $$3$$ $$\qquad$$ 33. $$−5$$ $$\qquad$$ 35. $$−\frac{17}{2}$$ $$\qquad$$ 37. $$ℝ$$ $$\qquad$$ 39. $$\frac{7}{8}$$ $$\qquad$$ 41. $$2.5$$ $$\qquad$$ 43. $$Ø$$ $$\qquad$$ 45. $$3$$ $$\qquad$$ 47. $$2$$ $$\qquad$$ 49. $$Ø$$
51. $$−\frac{5}{3}$$ $$\qquad$$ 53. $$−81$$ $$\qquad$$ 55. $$1.2$$ $$\qquad$$ 57. $$ℝ$$ $$\qquad$$ 59. $$0$$ $$\qquad$$ 61. $$Ø$$ $$\qquad$$ 63. $$\frac{6}{5}$$ $$\qquad$$ 65. $$ℝ$$ $$\qquad$$

### C: Solve Linear Formulas

Exercise $$\PageIndex{4}$$

$$\bigstar$$ Solve.

 Solve for $$w: P = 2l + 2w$$ Solve for $$a: P = a + b + c$$ Solve for $$t: D = rt$$ Solve for $$w: V = lwh$$ Solve for $$b: A = \dfrac{1}{2} bh$$ Solve for $$a:s = \dfrac{1}{2}at^{2}$$ Solve for $$a: A = \dfrac{1}{2}h (a + b)$$ Solve for $$h: V = \dfrac{1}{3}πr^{2}h$$ Solve for $$F: C = \dfrac{5}{9} (F − 32)$$ Solve for $$x: ax + b = c$$
67. $$w = \frac{P − 2l}{2}$$ $$\qquad$$ 69. $$t = \frac{D}{r}$$ $$\qquad$$ 71. $$b = \frac{2A}{h}$$ $$\qquad$$ 73. $$a = \frac{2A}{h} − b$$ $$\qquad$$ 75. $$F = \frac{9}{5} C + 32$$.