## Which are solutions of the equation 4×2 – 7x = 3x + 24? Check all that apply. x = –4 x = –3 x = -3/2 x = 2/3 x = 2 x = 4

Question

Which are solutions of the equation 4×2 – 7x = 3x + 24? Check all that apply. x = –4 x = –3 x = -3/2 x = 2/3 x = 2 x = 4

0

Given the equation:

rewrite the above equation as:

Like terms are those whose variables are same.

Combine like terms :

….[1]

Now, to solve the above quadratic equation:

For quadratic equation: where a,b, and c are constant.

then the solutions are:

…[2]

in equation [1], the values of a= 4, b=-10 and c= -24.

then, by putting these in the [2] we get,

On solving we get,  the solutions are:

and

Check :

By substituting the values of x= -1.5 and x=4 in equation   we have;

for x=-1.5

9+10.5=19.5

19.5=19.

Similarly, for x=4

64-28=36

36=36

Therefore, the only solution of the equation    is, x= -1.5 and x=4

2. 4×2 – 7x = 3x + 24
First we rewrite the quadratic equation:
4×2 – 7x – 3x – 24 = 0
4×2 – 10x – 24 = 0
The solutions to the quadratic equation in this case are:
x1 = 4
x2 = -1.5