Question

solve for x: 5 x + 7/2 is equal to 3/2x -14​

Answer 1

★ Solution :-

We have two methods to find the value of x in this question.

The first method is as follows

$\sf \leadsto 5x + \dfrac{7}{2} = \dfrac{3}{2}x - 14$

$\sf \leadsto \dfrac{10x + 7}{2} = \dfrac{3x - 28}{2}$

$\sf \leadsto 2(10x + 7) = 2(3x - 28)$

$\sf \leadsto 20x + 14 = 6x - 56$

$\sf \leadsto 20x - 6x = -56 - 14$

$\sf \leadsto 14x = -70$

$\sf \dashrightarrow x = \dfrac{-70}{14}$

$\sf \dashrightarrow x = -5$

$\:$

Now, we can find the value of x by the second method.

The second method is as follows

$\sf \leadsto 5x + \dfrac{7}{2} = \dfrac{3}{2}x - 14$

$\sf \leadsto 5x - \dfrac{3}{2}x = -14 - \dfrac{7}{2}$

$\sf \leadsto \dfrac{10x - 3x}{2} = \dfrac{-28 - 7}{2}$

$\sf \leadsto \dfrac{7x}{2} = \dfrac{-35}{2}$

$\sf \leadsto 2(7x) = 2(-35)$

$\sf \leadsto 14x = -70$

$\sf \leadsto x = \dfrac{-70}{14}$

$\sf \leadsto x = -5$

Therefore, the value of x is -5.

$\:$

Now let's check that, our answer is right or wrong.

$\sf \dashrightarrow 5x + \dfrac{7}{2} = \dfrac{3}{2}x - 14$

$\sf \leadsto 5(-5) + \dfrac{7}{2} = \dfrac{3(-5)}{2} - 14$

$\sf \leadsto -25 + \dfrac{7}{2} = \dfrac{-15}{2} - 14$

$\sf \leadsto \dfrac{-50 + 7}{2} = \dfrac{-15 - 28}{2}$

$\sf \dashrightarrow \dfrac{-43}{2} = \dfrac{-43}{2}$

Thus, we can conclude that the answer obtained is correct.

Answer 2

Answer:

$\underline{\purple{\ddot{\Mathsdude}}}$

♧♧To prove:-

• The value of x .

♧♧Explanation :-

• 5x+7/2=3/2x-14

• 10x+7/2=3x-28/2

• 2 (10x+7)=2 (3x-28)

• 20x+14=6x-56

• 20x-6x=-56-14

• 14x = -70

• x =-70/14

• x = -5.

The value of x is -5

♧♧Hope it helps u mate .

♧♧Thank you.