SOLUTION: Solve the inequality and graph the solution set on a number line. Be sure to use closed dots or open circles. Do not use parentheses or brackets.
25-x^2 > or equal to 0
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-> SOLUTION: Solve the inequality and graph the solution set on a number line. Be sure to use closed dots or open circles. Do not use parentheses or brackets.
25-x^2 > or equal to 0
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Question 1052674: Solve the inequality and graph the solution set on a number line. Be sure to use closed dots or open circles. Do not use parentheses or brackets.
the easiest way to solve these is to make the inequality an equation and solve for the equation and then determine the intervals for which the inequality is true.
set 25 - x^2 = 0.
add x^2 to both sides of the equation to get 25 = x^2.
solve for x to get x = plus or minus 5.
now look at the possible intervals created.
they are:
x < -5
x = -5
x > -5 and < 5
x = 5
x > 5
evaluate the equation in each of these intervals.
i chose the following values.
x = -6 for when x < -5
x = -5 for when x = -5
x = 0 for when x > -5 and < 5
x = 5 for when x = 5
x = 6 for when x > 5
when x = -6, 25 - x^2 becomes 25 - 36 which is less than 0.
when x = -5, 25 - x^2 becomes 25 - 25 which is equal to 0.
when x = 0, 25 - x^2 becomes 25 - 0 which is greater than 0.
when x = 5, 25 - x^2 becomes 25 - 25 which is equal to 0.
when x = 6, 25 - x^2 becomes 25 - 36 which is less than 0.
the problems states that 25 - x^2 is less than 0.
that happens when x <= -5 and when x >= 5.
those are your intervals when the stated inequality is true.
the graph of the equation is shown below.
your can see from the graph that 25 - x^2 <= 0 only when x <= -5 and when x >= 5.
your solution on the number line would look something like this:
