Exercice 23
1] 5 (2z - 1) = -2
a) Développer son premier membre : 5(2z - 1) = 10z - 5
b) 5(2z - 1) = -2
10z - 5 = - 2
10z = +5 - 2
10z = 3
z = [tex] \frac{3}{10} [/tex]
2] Résoudre
a) 3(x + 7) = 4
3x + 21 = 4
3x = -21 +4
3x = -17
x = [tex]- \frac{17}{3} [/tex]
b) 4a = 7(2a - 1)
4a = 14a - 7
4 + 7 = -4a + 14a
7 = +10 a
[tex] \frac{7}{10} [/tex] = a
exercice 24 - Résoudre chaque équation
a) 3(x + 7) = 4
3x + 21 = 4
3x = -17
x = [tex]- \frac{17}{3} [/tex]
b) 2(2 - y) = -6
4 - 2y = -6
4 + 6 = 2y
10 = 2y
[tex] \frac{10}{2} [/tex] = y
y = 5
c) -3 + a = 7(2a -1)
-3 + a = 14a - 7
-3 + 7 = -a + 14a
4 = +13a
[tex] \frac{4}{13} [/tex] = a
d) -3(2t + 1) = -3(t - 2)
-6t - 3 = -3t + 6
-6t + 3t = +3 +6
-3t = +9
t = [tex]- \frac{9}{3} [/tex]
t = - 3
Exercice 25 - Résoudre chaque équation
a) 2(x + 1) = 3(x - 1)
2x + 2 = 3x - 3
+2 +3 = -2x + 3x
5 = x
b) 3(2 - 3y) = -(y - 2)
6 - 9y = -y +2
6 - 2 = +9y - y
4 = 8y
[tex] \frac{4}{8} [/tex] = y
[tex] \frac{1}{2} = y [/tex]
c) -2(a - 1) = 4(2a + 1)
-2a + 2 = 8a + 4
+2 -4 = +2a + 8a
-2 = 10a
[tex]- \frac{2}{10} [/tex] = a
[tex]- \frac{1}{5} [/tex] = a
