Question 1:
Solve and check result: 3x = 2x + 18
Answer:
3x = 2x + 18
On transposing 2x to L.H.S, we obtain
3x − 2x = 18
x = 18
L.H.S = 3x = 3 × 18 = 54
R.H.S = 2x + 18 = 2 × 18 + 18 = 36 + 18 = 54
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Solve and check result: 3x = 2x + 18
Answer:
3x = 2x + 18
On transposing 2x to L.H.S, we obtain
3x − 2x = 18
x = 18
L.H.S = 3x = 3 × 18 = 54
R.H.S = 2x + 18 = 2 × 18 + 18 = 36 + 18 = 54
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Question 2:
Solve and check result: 5t − 3 = 3t − 5
Answer:
5t − 3 = 3t − 5
On transposing 3t to L.H.S and −3 to R.H.S, we obtain
5t − 3t = −5 − (−3)
2t = −2
On dividing both sides by 2, we obtain
t = −1
L.H.S = 5t − 3 = 5 × (−1) − 3 = −8
R.H.S = 3t − 5 = 3 × (−1) − 5 = − 3 − 5 = −8
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Solve and check result: 5t − 3 = 3t − 5
Answer:
5t − 3 = 3t − 5
On transposing 3t to L.H.S and −3 to R.H.S, we obtain
5t − 3t = −5 − (−3)
2t = −2
On dividing both sides by 2, we obtain
t = −1
L.H.S = 5t − 3 = 5 × (−1) − 3 = −8
R.H.S = 3t − 5 = 3 × (−1) − 5 = − 3 − 5 = −8
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Question 3:
Solve and check result: 5x + 9 = 5 + 3x
Answer:
5x + 9 = 5 + 3x
On transposing 3x to L.H.S and 9 to R.H.S, we obtain
5x − 3x = 5 − 9
2x = −4
On dividing both sides by 2, we obtain
x = −2
L.H.S = 5x + 9 = 5 × (−2) + 9 = −10 + 9 = −1
R.H.S = 5 + 3x = 5 + 3 × (−2) = 5 − 6 = −1
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Solve and check result: 5x + 9 = 5 + 3x
Answer:
5x + 9 = 5 + 3x
On transposing 3x to L.H.S and 9 to R.H.S, we obtain
5x − 3x = 5 − 9
2x = −4
On dividing both sides by 2, we obtain
x = −2
L.H.S = 5x + 9 = 5 × (−2) + 9 = −10 + 9 = −1
R.H.S = 5 + 3x = 5 + 3 × (−2) = 5 − 6 = −1
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Question 4:
Solve and check result: 4z + 3 = 6 + 2z
Answer:
4z + 3 = 6 + 2z
On transposing 2z to L.H.S and 3 to R.H.S, we obtain
4z − 2z = 6 − 3
2z = 3
Dividing both sides by 2, we obtain
z= 3/2
L.H.S = 4z + 3 = 4 × ( 3/2 ) + 3 = 6 + 3 = 9
R.H.S = 6 + 2z = 6 + 2 × ( 3/2 ) = 6 + 3 = 9
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Question 5:
Solve and check result: 2x − 1 = 14 − x
Answer:
2x − 1 = 14 − x
Transposing x to L.H.S and 1 to R.H.S, we obtain
2x + x = 14 + 1
3x = 15
Dividing both sides by 3, we obtain
x = 5
L.H.S = 2x − 1 = 2 × (5) − 1 = 10 − 1 = 9
R.H.S = 14 − x = 14 − 5 = 9
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Question 6:
Solve and check result: 8x + 4 = 3(x − 1) + 7
Answer:
8x + 4 = 3(x − 1) + 7
8x + 4 = 3x − 3 + 7
Transposing 3x to L.H.S and 4 to R.H.S, we obtain
8x − 3x = − 3 + 7 − 4
5x = − 7 + 7
x=0
L.H.S = 8x + 4 = 8 × (0) + 4 = 4
R.H.S = 3(x − 1) + 7 = 3 (0 − 1) + 7 = − 3 + 7 = 4
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Question 7:
Solve and check result: x = 4/5 ( x + 10 )
Answer:
x = 4/5 ( x + 10 )
Multiplying both sides by 5, we obtain
5x = 4(x + 10)
5x = 4x + 40
Transposing 4x to L.H.S, we obtain
5x − 4x = 40
x = 40
L.H.S = x = 40
RHS = x = 4/5 ( x + 10 )= 4/5 ( 40 + 10 ) = x = 4/5 ( 50 ) = 40
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Question 8:
Solve and check result: 2x/3 + 1 = 7x/15 + 3
Answer:
Transposing 7x/15 to L.H.S and 1 to R.H.S, we obtain
2x/3 - 7x/15= 3 - 1
3x/15 = 2
x/5 = 2
x=10
L.H.S = 2x/3 + 1 = 2×10/3 + 1 = 20+3/3 = 23/3
R.H.S = 7x/15 + 3 = 7×10/15 + 3 = ( 70 + 45 )/3 = 115/15 = 23/3
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Question 9:
Solve and check result: 2y + 5/3 = 26/3 - y
Answer:
2y + 5/3 = 26/3 - y
Transposing y to L.H.S and 5/3 to R.H.S, we obtain
2y + y = 26/3 - 5/3
3y = 21/3
3y = 21/3
y = 7/3
LHS= 2y + 5/3 = 2 × ( 7/3 ) + 5/3 = 14/3 + 5/3 = 19/3
RHS = 26/3 - y = 26/3 - 7/3 = = 19/3
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Question 10:
Solve and check result: 3m = 5m - 8/5
Answer:
3m = 5m - 8/5
Transposing 5m to L.H.S, we obtain
3m - 5m = - 8/5
-2m = - 8/5 Dividing both sides by −2, we obtain
m = 4/5
L.H.S = 3m = 3 × 4/5 = 12/5
R.H.S = 5m - 8/5 = 5 × 4/5 - 8/5 = 12/5
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Solve and check result: 4z + 3 = 6 + 2z
Answer:
4z + 3 = 6 + 2z
On transposing 2z to L.H.S and 3 to R.H.S, we obtain
4z − 2z = 6 − 3
2z = 3
Dividing both sides by 2, we obtain
z= 3/2
L.H.S = 4z + 3 = 4 × ( 3/2 ) + 3 = 6 + 3 = 9
R.H.S = 6 + 2z = 6 + 2 × ( 3/2 ) = 6 + 3 = 9
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Question 5:
Solve and check result: 2x − 1 = 14 − x
Answer:
2x − 1 = 14 − x
Transposing x to L.H.S and 1 to R.H.S, we obtain
2x + x = 14 + 1
3x = 15
Dividing both sides by 3, we obtain
x = 5
L.H.S = 2x − 1 = 2 × (5) − 1 = 10 − 1 = 9
R.H.S = 14 − x = 14 − 5 = 9
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Question 6:
Solve and check result: 8x + 4 = 3(x − 1) + 7
Answer:
8x + 4 = 3(x − 1) + 7
8x + 4 = 3x − 3 + 7
Transposing 3x to L.H.S and 4 to R.H.S, we obtain
8x − 3x = − 3 + 7 − 4
5x = − 7 + 7
x=0
L.H.S = 8x + 4 = 8 × (0) + 4 = 4
R.H.S = 3(x − 1) + 7 = 3 (0 − 1) + 7 = − 3 + 7 = 4
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Question 7:
Solve and check result: x = 4/5 ( x + 10 )
Answer:
x = 4/5 ( x + 10 )
Multiplying both sides by 5, we obtain
5x = 4(x + 10)
5x = 4x + 40
Transposing 4x to L.H.S, we obtain
5x − 4x = 40
x = 40
L.H.S = x = 40
RHS = x = 4/5 ( x + 10 )= 4/5 ( 40 + 10 ) = x = 4/5 ( 50 ) = 40
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Question 8:
Solve and check result: 2x/3 + 1 = 7x/15 + 3
Answer:
Transposing 7x/15 to L.H.S and 1 to R.H.S, we obtain
2x/3 - 7x/15= 3 - 1
3x/15 = 2
x/5 = 2
x=10
L.H.S = 2x/3 + 1 = 2×10/3 + 1 = 20+3/3 = 23/3
R.H.S = 7x/15 + 3 = 7×10/15 + 3 = ( 70 + 45 )/3 = 115/15 = 23/3
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Question 9:
Solve and check result: 2y + 5/3 = 26/3 - y
Answer:
2y + 5/3 = 26/3 - y
Transposing y to L.H.S and 5/3 to R.H.S, we obtain
2y + y = 26/3 - 5/3
3y = 21/3
3y = 21/3
y = 7/3
LHS= 2y + 5/3 = 2 × ( 7/3 ) + 5/3 = 14/3 + 5/3 = 19/3
RHS = 26/3 - y = 26/3 - 7/3 = = 19/3
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
Question 10:
Solve and check result: 3m = 5m - 8/5
Answer:
3m = 5m - 8/5
Transposing 5m to L.H.S, we obtain
3m - 5m = - 8/5
-2m = - 8/5 Dividing both sides by −2, we obtain
m = 4/5
L.H.S = 3m = 3 × 4/5 = 12/5
R.H.S = 5m - 8/5 = 5 × 4/5 - 8/5 = 12/5
L.H.S. = R.H.S.
Hence, the result obtained above is correct.
