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Réponse :
1) Solve the equations:
a) (5x + 14 = -6)
Solve for (x): [x = \frac{-6 - 14}{5} = -4]
Check: (5(-4) + 14 = -6)
b) (a - 12 = 5a - 2)
Solve for (a): [a = \frac{12 - 2}{5 - 1} = 2]
Check: (2 - 12 = 5(2) - 2)
c) (6(x + 2) = 4)
Solve for (x): [x = \frac{4}{6} - 2 = -\frac{1}{3}]
Check: (6\left(-\frac{1}{3} + 2\right) = 4)
d) (0 = 12 - 2(y - 3))
Solve for (y): [y = \frac{12}{2} + 3 = 9]
Check: (0 = 12 - 2(9 - 3))
e) (\frac{64}{m} = 4)
Solve for (m): [m = \frac{64}{4} = 16]
Check: (\frac{64}{16} = 4)
f) (-\frac{aima}{92813874} = 4)
Solve for (aima): [aima = -4 \times 92813874 = -371255496]
Check: (-\frac{371255496}{92813874} = 4)
2) Solve the simultaneous equations using the substitution method:
Given: [y = 4x - 1]
Substitute (y) into the second equation: [x + (4x - 1) = 26] [5x = 27] [x = \frac{27}{5} = 5.4]
Now find (y): [y = 4(5.4) - 1 = 21.6 - 1 = 20.6]
3) Solve the simultaneous equations using the elimination method:
Given: [x + y = 26] [x - y = 12]
Add the two equations to eliminate (y): [2x = 38] [x = 19]
Now find (y): [y = 26 - x = 26 - 19 = 7]
4) Solve the inequalities:
a) (2a + 3 < 7a)
Solve for (a): [a = \frac{3}{7 - 2} = \frac{3}{5}]
Check: (2\left(\frac{3}{5}\right) + 3 < 7\left(\frac{3}{5}\right))
b) (5b - 1 < b + 19)
Solve for (b): [b = \frac{19 + 1}{5 - 1} = 5]
Check: (5(5) - 1 < 5 + 19)
c) (3(c + 5) > 2(5c))
Solve for (c): [c = \frac{3 \times 5}{2 \times 5 - 3} = 3]
Check: (3(3 + 5) > 2(5 \times 3))
d) (4d \leq 7d + 15)
Solve for (d): [d = \frac{15}{7 - 4} = 5]
Check: (4(5) \leq 7(5) + 15)
5) Represent the inequalities on a number line:
a) (3) b) (-12 < 3n < 3)