Linear Equations in One Variable - 8th math
Solve the following equations and check your results
Question (1) 3x = 2 x + 18
Solution: Given,
3x = 2x + 18
After transposing 2x to LHS, we get
3x-2x=18
โ x = 18 Answer
Checking of result of Result
Given equation is 3x = 2x + 18
After substituting the value of x in LHS and RHS we get:
3 x = 2 ร 18 + 18
3 ร 18 = 36 + 18
3 ร 18 = 54
54 = 54
Thus, LHS = RHS
Question (2) 5t โ 3 = 3t โ 5
Solution:
Given, 5t โ 3 = 3t โ 5
After transposing 3t to LHS we get:
5t โ 3 โ 3t = โ5
After transposing โ3 to RHS we get
5t โ 3t =โ5 + 3
โ 2t = โ2
After transposing 2 to RHS, we get
โ 2t = โ2/2
โ t = โ1 Answer
Checking of Result
Given,
5t โ 3 = 3t โ 5
RHS = 3t โ 5
After substituting the value of t = โ1 which is calculated in the solution in RHS, we get
RHS = 3 ร (โ1) โ 5
= โ3 โ 5
โ RHS = โ8
LHS = 5t โ 3
After substituting the value of t = โ1 which is calculated in the solution in LHS, we get
LHS = 5(โ1) โ 3
= โ5 โ 3
โ LHS = โ8
Thus, LHS = RHS proved
Question (3) 5x + 9 = 5 + 3x
Solution:
Given, 5x + 9 = 5 + 3x
After transposing 9 to RHS, we get
โ 5x = 5 + 3x โ 9
And, after transposing 3x to LHS, we get
โ 5x โ 3x = 5 โ 9
โ 2x = โ4
After dividing both sides by 2, we get
โ 2x/2 = โ4/2
โ x = โ2 Answer
CHECKING OF RESULT:
Given, 5x + 9 = 5 + 3x
LHS = 5x + 9
After substituting the value of x = โ2, we get
LHS = 5 (โ2) + 9
= โ10 + 9
โ LHS = โ1
Now, RHS = 5 + 3x
After substituting the value of x = โ2, we get
LHS = 5 + 3 (โ2)
= 5 + (โ6)
= 5 โ 6
โ LHS = โ1
Thus, LHS = RHS Proved
Question (4) 4x + 3 = 6 + 2x
Solution:
Given, 4x + 3 = 6 + 2x
After transposing 3 to RHS, we get
4x = 6 + 2x โ 3
Now, after transposing 2x to LHS, we get
4x โ 2x = 6 โ 3
โ 2x = 3
After dividing both sides by 2 we get
โ (2x)/2 = 3/2
โ x = 3/2 Answer
CHECKING OF RESULT:
Given, 4x + 3 = 6 + 2x
LHS = 4x + 3
Substituting the value of x = 3/2 in LHS we get
= 4 ร 3/2 + 3
= 2 ร 3 + 3
= 6 + 3 = 9
โ LHS = 9
Now, RHS = 6 + 2x
Substituting the value of x = 3/2 in RHS we get
= 6 + 2 ร 3/2
= 6 + 3 = 9
โ RHS = 9
Thus, LHS = RHS proved
Question (5) 2x โ 1 = 14 โ x
Solution:
Given, 2x โ 1 = 14 โ x
After transposing โ1 to RHS, we get
2x = 14 โ x + 1
After transposing โx to LHS, we get
2x + x = 14 + 1
3x = 15
After transposing 3 to RHS, we get
x = 15/3 = 5
Thus, x = 5 Answer
CHECKING OF RESULT:
Given, 2x โ 1 = 14 โ x
Now, LHS =2x โ 1
After substituting the value of x = 5 in LHS we get
2 ร 5 โ1
= 10 โ 1
Thus, LHS = 9
Now, RHS = 14 โ x
After substituting the value of x = 5 in RHS we get
= 14 โ 5
โ RHS= 9
Thus, LHS = RHS proved
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