Solve the inequality symbolically and write your solution in interval notation. -7 ≤ 4 – 3x < 7

Question

Solve the inequality symbolically and write your solution in interval notation. -7 ≤ 4 – 3x < 7

Answer 1

7 >= 3x-4 > -7 <--- multiplies by -1; all signs switch

11 >= 3x >= -3 <--- adds 4

11/3 >= x >= -1 <-- divides by 3

which is the same as:

-1 <=x <= 11/3

[-1, 11/3]

closed circles (I call them meatballs) at -1 and 11/3

shades in between

note that for x=0, the statement is true.

but for x = -2, the statement 10<7 is false

and for x=5, the statement -7 <= -11 is also false

this checks the answer, shown above in bold