Answer:
a) x = 12
b) y = -2
c) a = 3
d) x = -1/24
e) x = -21
Step-by-step explanation:
[tex]a) \ \dfrac{5 \cdot x}{6} =10[/tex]
Multiply both sides by 6
[tex]\therefore \dfrac{5 \cdot x}{6} \times 6 =10 \times 6[/tex]
6/6 = 1
∴ 5·x × 1 = 10 × 6 = 60
x = 60/5 = 12
x = 12
b) -8.3·y - 2.3 = 14.3
Add 2.3 to both sides
-8.3·y + (- 2.3 + 2.3) = 14.3 + 2.3
-8.3·y + 0 = 16.6
Divide both sides by (-8.3)
-8.3·y/(-8.3) = 16.6/(-8.3)
-8.3·y/(-8.3) = y·(-8.3)/(-8.3) = y × 1 = y = 16.6/(-8.3) = -2
∴ y = -2
c) 7·a - 1 = a + 17
Subtract 'a' from both sides gives;
7·a - 1 - a = a + 17 - a
7·a - 1 - a = a + 17 - a = a - a + 17 = 17
7·a - 1 - a = 7·a - a - 1 = 6·a - 1 = 17
Add 1 to both sides gives;
6·a - 1 + 1 = 17 + 1 = 18
6·a - 1 + 1 = 6·a + 0 = 18
6·a = 18
a = 18/6 = 3
∴ a = 3
d) -6·x = (1/4)
Divide both sides by (-6) gives;
-6·x/(-6) = (1/4)/(-6) = 1/(4 × (-6)) = -1/24
∴ x = -1/24
e) 6·x + 2 = -19 + 5·x
Subtract 5·x + 2 from both sides gives;
6·x + 2 - (5·x + 2) = -19 + 5·x - (5·x + 2)
6·x - 5·x + 2 - 2= -19 - 2 + 5·x - 5·x
x = -21.
