Question

Solve each of the following equations and check your solution by substituting in the equation.
(1) 6x-9-2(1+x)=x-9
(2) 2(x+2)+5(x+5)=4(x-8)+2(x-2)
(3) (3+x)/(2x-3)=-1/2​

Answer 1

Answer:

given,

1) 6x - 9 - 2(1 + x ) = x - 9

2) 2 (x + 2) + 5( x + 5 ) = 4 ( x - 8 ) + 2 ( x - 2 )

3) ( 3 + x )/ (2x - 3 ) = - 1/2.

to find : -

value of x.

$\sf\underline{solution}$

1) 6x - 9 - 2(1 + x ) = x - 9

6x - 9 - 2 - 2x = x - 9

4x - 11 = x - 9

4x - x = - 9 + 11

3x = 2.

x = $\sf\dfrac{2}{3}$

2) 2 (x + 2) + 5( x + 5 ) = 4 ( x - 8 ) + 2 ( x - 2 )

2x + 4 + 5x + 25 = 4x - 32 + 2x - 4

7x + 29 = 6x - 36

7x - 6x = -36 - 29

x = - 65

3) ( 3 + x )/ (2x - 3 ) = - 1/2

(3 + x ) × 2 = - 1 × (2x - 3)

6 + 2x = -2x + 3

2x + 2x = 3 - 6

4x = -3

x = $\sf\dfrac{-3}{4}$

Verification :-

1) x = $\sf\dfrac{2}{3}$

6x - 9 - 2(1 + x ) = x - 9

6 × 2/3 - 9 - 2( 1 + 2/3) = 2/3 - 9

4 - 9 - 2(5/3) = -25/3

4 - 9 - 10/3 = -25/3

-5 - 10/3 = -25/3

-25/3 = -25/3

hence "verified ".

2) x = - 7

2 (x + 2) + 5( x + 5 ) = 4 ( x - 8 ) + 2 ( x - 2 )

2( -65+2) + 5(-65+5) = 4(-65-8) + 2 (-65-2)

2×-63+5×-60 = 4×-73 + 2×-67

- 126 - 300 = -292 - 134

-426 = -426.

"Hence verified"

3) x = $\sf\dfrac{-3}{4}$

( 3 + x )/ (2x - 3 ) = - 1/2.

(3 + -3/4) / (2×-3/4 - 3) = -1/2

( 9/4)/(-3/2-3) = -1/2

(9/4)/(-9/2) = -1/2

-1/2 = -1/2

"Hence verified"