Question

How many solutions can be found for the equation −4x − 11 = 2(x − 3x) + 13?

Answer 1

Answer:

The Equation is

- 4 x - 11 = 2 (x - 3 x) + 13

→ - 4 x - 11= 2 x - 2* 3 x + 13⇒⇒Using Distributive property of multiplication over subtraction which is , A * (B - C) = A*B - A*C

Bringing variables on one side and Constants on another side

→ - 4 x - 2 x + 6 x = 13 +11

→ - 6 x + 6 x = 24

0 =24

which is not possible.

Hence this equation has no solution.

If you look at the equation in the way

L HS= - 4 x - 11

A= - 4 x -11

R H S = 2 *(x - 3 x) + 13

B= 2 * (- 2 x) +13

 = - 4 x + 13

Both L HS and R H S, if looked individually represent lines in two dimensional plane, having equal slopes and different Y intercept.

So, the two lines are parallel.

Parallel lines do not intersect.

So, the equation has no solution.

Answer 2

-4x - 11 = 2(x - 3x) + 13
-4x - 11 = 2x - 6x + 13
-4x - 11 = -4x + 13
-4x + 4x = 13 + 11
0 = 24...incorrect......no solutions for this problem