Question

Solve the following equation and check your solution: 9x + 7 = 2( 3x - 5)​

Answer 1

Answer:

we have,

(9x-7)/(3x+5) = (3x-4)/(x+6)

(9x-7)/(3x+5) – (3x-4)/(x+6) = 0

By taking LCM as (3x+5) (x+6)

((9x-7) (x+6) – (3x-4) (3x+5)) / (3x+5) (x+6) = 0

By cross-multiplying we get,

(9x-7) (x+6) – (3x-4) (3x+5) = 0

Upon expansion we get,

9x2 + 54x – 7x – 42 – (9x2 + 15x – 12x – 20) = 0

44x – 22 = 0

44x = 22 x = 22/44 = 2/4 = 1/2

Now let us verify the given equation,

(9x-7)/(3x+5) = (3x-4)/(x+6)

By substituting the value of ‘x’ we get,

(9(1/2) – 7) / (3(1/2) + 5) = (3(1/2) – 4) / ((1/2) + 6)

(9/2 – 7) / (3/2 + 5) = (3/2 – 4) / (1/2 + 6)

((9-14)/2) / ((3+10)/2) = ((3-8)/2) / ((1+12)/2)

-5/2 / 13/2 = -5/2 / 13/2

-5/13 = -5/13

Hence, the given equation is verified.

Answer 2

Step-by-step explanation:

9x + 7 = 2( 3x - 5)----------1

9x + 7 = 6x - 10

9x - 6x = -10 -7

3x = -17

$x = \frac{ - 17}{3} \: \: \: \: (putting \: in \: 1)$

$9 \times \frac{ - 17}{3} + 7 = 2(3 \times \frac{ - 17}{3} - 5)$

$\frac{ - 153}{3} + 7 = 2( \frac{ - 51}{3} - 5)$

$\frac{ - 153 + 21}{3} = 2( \frac{ - 51 - 15}{3} )$

$\frac{ - 132}{3} = 2( \frac{ - 66}{3} )$

$\frac{ - 132}{2} = \frac{ - 132}{2}$

hence verified