Solve the Equations

(i) 5x = 3x + 24 (ii) 8t + 5 = 2t – 31

(iii) 7x – 10 = 4x + 11 (iv) 4z + 3 = 6 + 2z

(v) 2x – 1 = 14 – x (vi) 6x + 1 = 3(x – 1) + 7

(vii) (viii)

(ix)3(x + 1) = 12 + 4(x – 1) (x) 2x – 5 = 3(x – 5)

(xi) 6(1 – 4x) + 7(2 + 5x) = 53 (xii) 3(x + 6) + 2(x + 3) = 64

(xiii) (xiv) (3/4) ( x - 1) = (x - 3)

Note: In This part, our main objective would be to bring variables to one side of the equation and numbers to another side.

(i) 5x = 3x + 24

⇒ 5x - 3x = 24

⇒ 2x = 24

⇒ x = 12

(ii) 8t + 5 = 2t – 31

⇒ 8t - 2t = - 31 - 5

⇒ 6t = - 36

⇒ t = - 6

(iii) 7x – 10 = 4x + 11

⇒ 7x - 4x = 10 + 11

⇒ 3x = 21

⇒ x = 7

(iv) 4z + 3 = 6 + 2z

⇒ 4z - 2z = 6 - 3

⇒ 2z = 3

(v) 2x – 1 = 14 – x

⇒ 2x + x = 14 + 1

⇒ 3x = 15

⇒ x = 5

(vi) 6x + 1 = 3(x – 1) + 7

⇒ 6x + 1 = 3x - 3 + 7

⇒ 6x - 3x = - 1 - 3 + 7

⇒ 3x = 3

⇒ x = 1

(vii)

We can make it simple by eliminating fractions and making it as a equation of integers only

For this we should multiply all terms of the equation with an appropriate numbers

Our Purpose is to eliminate the denominators, so the number we choose to multiply has to be a multiple of the denominator, this has to satisfy all denominators. Hence, we choose that Number to be the L.C.M. of all numbers in denominator.

So. in this question, it has to be L.C.M. of 5 & 2 that is 10.

So, multiply all terms of equation with 10

⇒ 4x - 15 = 5x + 10

⇒ 4x - 5x = 15 + 10

⇒ - x = 25

⇒ x = - 25

(viii)

Multiply with L.C.M. of 5 & 1 that is 5

⇒ x - 3 - 10 = 2x

⇒ x - 2x = 13

⇒ - x = 13

⇒ x = - 13

(ix)3(x + 1) = 12 + 4(x – 1)

⇒ 3x + 3 = 12 + 4x - 4

⇒ 3x - 4x = 12 - 4 - 3

⇒ - x = 5

⇒ x = - 5

(x) 2x – 5 = 3(x – 5)

⇒ 2x - 5 = 3x - 15

⇒ 2x - 3x = 5 - 15

⇒ - x = - 10

⇒ x = 10

(xi) 6(1 – 4x) + 7(2 + 5x) = 53

⇒ 6 - 24x + 14 + 35x = 53

⇒ 35x - 24x = 53 - 6 - 14

⇒ 11x = 33

⇒ x = 3

(xii) 3(x + 6) + 2(x + 3) = 64

⇒ 3x + 18 + 2x + 6 = 64

⇒ 5x + 24 = 64

⇒ 5x = 64 - 24

⇒ 5x = 40

⇒ x = 8

(xiii)

Multiplying with L.C.M. of 3 & 2, that is 6

⇒ 4m + 48 = 3m - 6

⇒ 4m - 3m = - 48 - 6

⇒ m = - 54

(xiv) (3/4) ( x - 1) = (x - 3)

⇒3 (x - 1) = 4 (x - 3)

⇒ 3x - 3 = 4x - 12

⇒ x = 9