Final answer:
The value of x can be any real number.
Step-by-step explanation:
To find the value of x, we need to solve the equation 7(a+b)=<-35, 28>. First, let's substitute the given values of a and b. We have a = <-4, 1> and b = <-1, x>. Plugging these values into the equation, we get 7(<-4, 1> + <-1, x>) = <-35, 28>.
Simplifying the expression on the left side, we get 7<-5, 1+x> = <-35, 28>. This can be further simplified as <-35, 7+7x> = <-35, 28>. Now, we can equate the x-coordinates and y-coordinates separately.
Equating the x-coordinates, we have -35 = -35, which is true for any value of x. Therefore, the value of x can be any real number.
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