Solve the following linear equations.
1. x/2 – 1/5 = x/3 + ¼
Solution:
Given, x/2 – 1/5 = x/3 + ¼
Now,
x/2 – x/3 = ¼+ 1/5
(3x – 2x)/6 = (5 + 4)/20
3x – 2x = 9/20 × 6
x = 54/20
x = 27/10
2. n/2 – 3n/4 + 5n/6 = 21
Solution:
Given, n/2 – 3n/4 + 5n/6 = 21
Now,
(6n – 9n + 10n)/12 = 21
7n/12 = 21
7n = 21 × 12
n = 252/7
n = 36
3. x + 7 – 8x/3 = 17/6 – 5x/2
Solution:
Given, x + 7 – 8x/3 = 17/6 – 5x/2
Now,
x – 8x/3 + 5x/2 = 17/6 – 7
(6x – 16x + 15x)/6 = (17 – 42)/6
5x/6 = – 25/6
5x = – 25
x = – 5
4. (x – 5)/3 = (x – 3)/5
Solution:
Given, (x – 5)/3 = (x – 3)/5
Now,
5(x-5) = 3(x-3)
5x-25 = 3x-9
5x – 3x = -9+25
2x = 16
x = 8
5. (3t – 2)/4 – (2t + 3)/3 = 2/3 – t
Solution:
Given, (3t – 2)/4 – (2t + 3)/3 = 2/3 – t
Now,
((3t – 2)/4) × 12 – ((2t + 3)/3) × 12
(3t – 2) × 3 – (2t + 3) × 4 = 2 × 4 – 12t
9t – 6 – 8t – 12 = 8 – 12t
9t – 6 – 8t – 12 = 8 – 12t
t – 18 = 8 – 12t
t + 12t = 8 + 18
13t = 26
t = 2
6. m – (m – 1)/2 = 1 – (m – 2)/3
Solution:
Given, m – (m – 1)/2 = 1 – (m – 2)/3
Now,
m – m/2 – 1/2 = 1 – (m/3 – 2/3)
m – m/2 + ½ = 1 – m/3 + 2/3
m – m/2 + m/3 = 1 + 2/3 – ½
m/2 + m/3 = ½ + 2/3
(3m + 2m)/6 = (3 + 4)/6
5m/6 = 7/6
m = 7/6 × 6/5
m = 7/5
Simplify and solve the following linear equations.
7. 3(t – 3) = 5(2t + 1)
Solution:
Given, 3(t – 3) = 5(2t + 1)
Now,
3t – 9 = 10t + 5
3t – 10t = 5 + 9
-7t = 14
t = 14/-7
t = -2
8. 15(y – 4) –2(y – 9) + 5(y + 6) = 0
Solution:
Given, 15(y – 4) –2(y – 9) + 5(y + 6) = 0
Now,
15y – 60 -2y + 18 + 5y + 30 = 0
15y – 2y + 5y = 60 – 18 – 30
18y = 12
y = 12/18
y = 2/3
9. 3(5z – 7) – 2(9z – 11) = 4(8z – 13) – 17
Solution:
Given, 3(5z – 7) – 2(9z – 11) = 4(8z – 13) – 17
Now,
15z – 21 – 18z + 22 = 32z – 52 – 17
15z – 18z – 32z = -52 – 17 + 21 – 22
-35z = -70
z = -70/-35
z = 2
10. 0.25(4f – 3) = 0.05(10f – 9)
Solution:
Given, 0.25(4f – 3) = 0.05(10f – 9)
Now,
f – 0.75 = 0.5f – 0.45
f – 0.5f = -0.45 + 0.75
0.5f = 0.30
f = 0.30/0.5
f = 3/5
f = 0.6
👍👍👍
