Question

Solve for x and draw the graph in xy plane.i) 24 - 3 ( x - 2 ) = x + 18ii) 3x + 2/7 + 4 (x+1) /5 = 2 / 3 (2x+1)iii) x-1/3 - 1/4(x-2) = 1iv) (3x -7)/5 - x+1/6= 2x +2/12 -1please answer my question ​

Answer 1

Linear equations & graphs

(i)

The given equation is

24 - 3 (x - 2) = x + 18

or, 24 - 3x + 6 = x + 8

or, 3x + x = 24 + 6 - 8

or, 4x = 22

or, x = 11

(ii)

The given equation is

(3x + 2)/7 + 4 (x + 1)/5 = 2/3 * (2x + 1)

or, (15x + 10 + 28x + 28)/35 = 2/3 * (2x + 1)

or, (43x + 38)/35 = (4x + 2)/3

or, 129x + 114 = 140x + 70

or, 11x =44

or, x = 4

(iii)

The given equation is

x - 1/3 - 1/4 * (x - 2) = 1

or, (4x - 4 - 3x + 6)/12 = 1

or, (x + 2)/12 = 1

or, x + 2 = 12

or, x = 10

(iv)

The given equation is

(3x - 7)/5 - (x + 1)/6 = (2x + 2)/12

or, (18x - 42 - 5x - 5)/42 = (x + 1)/6

or, (13x - 47)/7 = x + 1

or, 13x - 47 = 7x + 7

or, 6x = 54

or, x = 9

Drawing graphs:

We have found four straight lines x = 11, x = 4, x = 10 and x = 9, and they all are parallel to the y-axis.

[ See the given attachment for graphs. ]