To solve linear equations with rational coefficients, we have to know operations on fractions.
Solve each equation.
Problem 1 :
m + 4 = 13/2
Solution :
m + 4 = 13/2
Subtract 4 from each side.
m + 4 - 4 = (13/2) – 4
m = (13 – 8)/2
m = 5/2
Problem 2 :
8/3 = x – 1 1/3
Solution :
8/3 = x – 1 1/3
8/3 = x – 4/3
Adding 4/3 on both side.
8/3 + 4/3 = 4/3 + x – 4/3
12/3 = x
4 = x
Problem 3 :
4/5 + v = 41/20
Solution :
4/5 + v = 41/20
Subtract 4/5 from each side.
4/5 + v – 4/5 = 41/20 – 4/5
v = 41/20 – 4/5 × (4/4)
v = 41/20 – 16/20
v = 25/20
v = 5/4
Problem 4 :
-11/5 = -2 + n
Solution :
-11/5 = -2 + n
Adding 2 on each side.
-11/5 + 2 = -2 + n + 2
(-11 + 10)/5 = n
-1/5 = n
Problem 5 :
-17/4 = v - 2
Solution :
-17/4 = v - 2
Adding 2 on each side.
-17/4 + 2 = v – 2 + 2
(-17 + 8)/4 = v
-9/4 = v
Problem 6 :
x + 1 = 11/5
Solution :
x + 1 = 11/5
Subtract 1 from each side.
x + 1 – 1 = 11/5 - 1
x = (11 – 5)/5
x = 6/5
Problem 7 :
(2/3)x = -1
Solution :
(2/3)x = -1
Multiplying both side by 3.
(2/3)x . 3 = -1.3
2x = -3
Divide each side by 2.
2x/2 = -3/2
x =-3/2
Problem 8 :
-3/2 = -3/2x
Solution :
-3/2 = (-3/2)x
Multiplying both side by 2.
(-3/2) . 2 = (-3/2) . 2
-3 = -3x
Divide each side by 3.
-3/3 = -3x/3
-1 = -x
x = 1
Problem 9 :
(2/5)x = -1/10
Solution :
(2/5)x = -1/10
Using cross multiplication.
20x = -5
Diving by 20
x = -1/4
Problem 10 :
-9/4 = -5x/4
Solution :
-9/4 = -5x/4
Multiplying both side by 4.
(-9/4) . 4 = (-5x/4) . 4
-9 = -5x
Divide each side by -5.
-9/(-5) = -5x/(-5)
9/5 = x
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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