1. let x[n] be a signal with x[n] = 0 for n< -1 and n > 3. for each signal given below, determine the values of n for which it is guaranteed to be zero. (a) x [n -2] (b) x [n+ 3] (c) x [-n + 1]

a) n<1 and n>5

b)  0 < n < -4

c)  n > 2 and n < -2

Step-by-step explanation:

The signal is given by x[n] = 0 for n < -1 and n > 3

The problem asks us to determine the values of n for which it's guaranteed to be zero.

a) x[n-2]

We know that n -2 must be less than -1 or greater than 3.

Therefore we're going to write down our inequalities and solve for n

Therefore for n<1 and n>5 x [n-2] will be zero

b) x [n+ 3]

Similarly, n + 3 must be less than -1 or greater than 3

Therefore for n< -4 and n>0, in other words, for 0 < n < -4  x[n-2] will be zero

c)x [-n + 1]

Similarly, -n+1 must be less than -1 or greater than 3

Therefore, for n > 2 and n < -2  x[-n+1] will be zero

a is the correct

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3