Question

solve for the variable.

1. \\(\frac{c}{3} = 9\\)
2. \\(k - 12 = -10\\)
3. \\(a + 53 \le -60\\)
4. \\(42 > x - 25\\)
5. \\(-37 = x + 9.9\\)
6. \\(y - (-13) = 49\\)
7. \\(2x = -16\\)
8. \\(-4y > 88\\)
9. \\(\frac{m}{15} = 2\\)
10. \\(-4x + 7.2 = 32\\)
11. \\(7x - 3 = -9\\)
12. \\(8.4 - 2x < 16\\)
13. \\(7.5 - x = 26.8\\)
14. \\(-3x + 18 = -27\\)
15. \\(15x - 6 \ge -21\\)
16. \\(-4x + 8 = 40\\)
17. \\(\frac{x}{7} - 2 = 8\\)
18. \\(\frac{x}{6} + 9 \le 10\\)

Explanation:

Identify the given problems

We have 18 independent equations and inequalities to solve for the variable.

Solve questions 1 to 6

Using the Solving Linear Inequalities knowledge point for inequalities, and standard algebraic operations for equations:

1. \(\frac{c}{3} = 9 \implies c = 27\)
2. \(k - 12 = -10 \implies k = 2\)
3. Using the Solving Linear Inequalities knowledge point

$$ a + 53 \le -60 \implies a \le -113 $$

1. Using the Solving Linear Inequalities knowledge point

$$ 42 > x - 25 \implies 67 > x \implies x < 67 $$

1. \(-37 = x + 9.9 \implies x = -46.9\)
2. \(y - (-13) = 49 \implies y + 13 = 49 \implies y = 36\)

Solve questions 7 to 12

1. \(2x = -16 \implies x = -8\)
2. Using the Solving Linear Inequalities knowledge point

$$ -4y > 88 \implies y < -22 $$

1. \(\frac{m}{15} = 2 \implies m = 30\)
2. \(-4x + 7.2 = 32 \implies -4x = 24.8 \implies x = -6.2\)
3. \(7x - 3 = -9 \implies 7x = -6 \implies x = -\frac{6}{7}\)
4. Using the Solving Linear Inequalities knowledge point

$$ 8.4 - 2x < 16 \implies -2x < 7.6 \implies x > -3.8 $$

Solve questions 13 to 18

1. \(7.5 - x = 26.8 \implies -x = 19.3 \implies x = -19.3\)
2. \(-3x + 18 = -27 \implies -3x = -45 \implies x = 15\)
3. Using the Solving Linear Inequalities knowledge point

$$ 15x - 6 \ge -21 \implies 15x \ge -15 \implies x \ge -1 $$

1. \(-4x + 8 = 40 \implies -4x = 32 \implies x = -8\)
2. \(\frac{x}{7} - 2 = 8 \implies \frac{x}{7} = 10 \implies x = 70\)
3. Using the Solving Linear Inequalities knowledge point

$$ \frac{x}{6} + 9 \le 10 \implies \frac{x}{6} \le 1 \implies x \le 6 $$

Answer:

No.	Answer
2	\(k = 2\)
3	\(a \le -113\)
4	\(x < 67\)
5	\(x = -46.9\)
6	\(y = 36\)
7	\(x = -8\)
8	\(y < -22\)
9	\(m = 30\)
10	\(x = -6.2\)
11	\(x = -\frac{6}{7}\)
12	\(x > -3.8\)
13	\(x = -19.3\)
14	\(x = 15\)
15	\(x \ge -1\)
16	\(x = -8\)
17	\(x = 70\)
18	\(x \le 6\)