Question

exercises 10-3

solve each of the following equations.

1. \\(12b + 1 = -71\\)
2. \\(\frac{a + 4}{8} = 2\\)
3. \\(45 = 6x - 9\\)
4. \\(35 - 3c = -10\\)
5. \\(2x^2 = 32\\)
6. \\(-10 - 5c = 20\\)
7. \\(8x + 4 = -14 + 2x\\)
8. \\(5 + 9a = 7a + 11\\)
9. \\(\frac{b}{-7} + 1 = -1\\)
10. \\(9(2n + 3) = 18\\)
11. \\(-4b + 2 = -98\\)
12. \\(10 = 3(6 + 8n)\\)
13. \\(2q + 10 = -5q + 3\\)
14. \\(\frac{r + 5}{3} = 17\\)
15. \\(x^2 - 5 = 44\\)
16. \\(12 = -6(c + 1)\\)
17. \\(3a^2 - 4 = 104\\)
18. \\(5 +

\frac{c}{3} = -10\\)

Explanation:

Solve linear equations with one variable

Using the Linear Equations Solving knowledge point, we isolate the variable by performing inverse operations.

For Question 1:

$$ 12b + 1 = -71 \implies 12b = -72 \implies b = -6 $$

For Question 2:

$$ \frac{a + 4}{8} = 2 \implies a + 4 = 16 \implies a = 12 $$

For Question 3:

$$ 45 = 6x - 9 \implies 54 = 6x \implies x = 9 $$

For Question 4:

$$ 35 - 3c = -10 \implies -3c = -45 \implies c = 15 $$

For Question 6:

$$ -10 - 5c = 20 \implies -5c = 30 \implies c = -6 $$

For Question 7:

$$ 8x + 4 = -14 + 2x \implies 6x = -18 \implies x = -3 $$

For Question 8:

$$ 5 + 9a = 7a + 11 \implies 2a = 6 \implies a = 3 $$

For Question 9:

$$ \frac{b}{-7} + 1 = -1 \implies \frac{b}{-7} = -2 \implies b = 14 $$

For Question 10:

$$ 9(2n + 3) = 18 \implies 2n + 3 = 2 \implies 2n = -1 \implies n = -\frac{1}{2} $$

For Question 11:

$$ -4b + 2 = -98 \implies -4b = -100 \implies b = 25 $$

For Question 12:

$$ 10 = 3(6 + 8n) \implies 10 = 18 + 24n \implies -8 = 24n \implies n = -\frac{1}{3} $$

For Question 13:

$$ 2q + 10 = -5q + 3 \implies 7q = -7 \implies q = -1 $$

For Question 14:

$$ \frac{r + 5}{3} = 17 \implies r + 5 = 51 \implies r = 46 $$

For Question 16:

$$ 12 = -6(c + 1) \implies -2 = c + 1 \implies c = -3 $$

For Question 18:

$$ 5 + \frac{c}{3} = -10 \implies \frac{c}{3} = -15 \implies c = -45 $$

Solve quadratic equations

Using the Quadratic Equations Solving knowledge point, we isolate the squared term and take the square root.

For Question 5:

$$ 2x^2 = 32 \implies x^2 = 16 \implies x = \pm 4 $$

For Question 15:

$$ x^2 - 5 = 44 \implies x^2 = 49 \implies x = \pm 7 $$

For Question 17:

$$ 3a^2 - 4 = 104 \implies 3a^2 = 108 \implies a^2 = 36 \implies a = \pm 6 $$

Answer:

No.	Answer
2	\(a = 12\)
3	\(x = 9\)
4	\(c = 15\)
5	\(x = \pm 4\)
6	\(c = -6\)
7	\(x = -3\)
8	\(a = 3\)
9	\(b = 14\)
10	\(n = -\frac{1}{2}\)
11	\(b = 25\)
12	\(n = -\frac{1}{3}\)
13	\(q = -1\)
14	\(r = 46\)
15	\(x = \pm 7\)
16	\(c = -3\)
17	\(a = \pm 6\)
18	\(c = -45\)