A binary operation * is defined on R the set of real numberr by x*y=x-2y for all a ,y e R if (4*q)*8=6 find q
x*y=x-2y
then (4*q) = 4 - 2q
and then
(4*q)*8 = 4*q - 16
= (4-2q) - 16
= -2q - 12
but this equals 6
-2q - 12 = 6
-2q = 18
q = -9
check
(4*-9)*8 = (4 - 2(-9))*8 = 22*8
= 22-16 = 6
To find the value of q, we'll substitute the given expression into the definition of the binary operation * and solve for q.
Given: (4*q)*8 = 6
According to the definition, we have:
(4*q) - 2 * 8 = 6
Now, let's simplify the equation:
4*q - 16 = 6
To isolate q, we'll move the constant term to the other side of the equation:
4*q = 6 + 16
4*q = 22
Finally, divide both sides of the equation by 4:
q = 22 / 4
q = 5.5
Therefore, the value of q is 5.5.
To find the value of q, we need to substitute the given values into the expression and solve for q.
First, let's substitute the given values into the expression:
(4*q)*8 = 6
Now, let's use the definition of the binary operation *: x*y = x - 2y.
For our expression, it becomes:
(4*q) - 2(8) = 6
Simplify the equation:
4q - 16 = 6
Next, isolate the q term:
4q = 6 + 16
4q = 22
Finally, solve for q by dividing both sides of the equation by 4:
q = 22/4
q = 5.5
Therefore, q equals 5.5.