Lisa's Responses in WyzAnt Answers

-x + 3 > 7

-x + 3 - 3 > 7 - 3    This step is straightforward and the same as an equality.

-x > 4    It's this next step that confuses a lot of students.

-x/-1 < 4/-1   When you divide out the negative, you flip the sign

So the solution is x < -4

To understand why, it helps if you draw a number line and think about what it means. If negative x is greater than 4, x itself must be a negative number and has to be less than -4.

(x)...(-4)...(-3)...(-2)...(-1)...(0)...(1)...(2)...(3)...(4)...(-x)

See Nataliya's answer for the full explanation. The key point where you went wrong was on b². The b value is -1, which means the entire value including the negative sign is being squared, (-1)²=1. So the value under the radical should have been 1+80=81 and you accidentally ended up with -1+80=79.

To do this, you need to know what fraction the wedge represents, which should be given as part of the problem. Either the wedge is defined as being 1/6 or 1/8 or something like that, or the length of the arc segment will be given so that you can compare it to the perimeter to determine this.

For instance, if the perimeter is given as 40 and the arc is length 8, you know the area of that wedge represents 1/5th of the whole disc.

Multiply the area of the segment to work out the area of the whole circle. Then just plug your number into the formula of an area of a circle and solve for the radius. (Divide out pi to find r^2 and take the square root to get r.)