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
Algebra.Com
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.
25-x^2 > or equal to 0
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your equation is 25 - x^2 >= 0
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:
RELATED QUESTIONS
Solve the inequality and graph the solution set on a number line. Be sure to use closed... (answered by Fombitz)
Solve the inequality and graph the solution set on a number line. Be sure to use closed... (answered by Fombitz)
During the tax-free weekend sales, Isabel wants to use a $50 gift card to purchase... (answered by Theo)
Solve the compound inequality and graph the solution.
u+6 ≥ 1 and u-3<2
i know... (answered by stanbon)
solve the compound inequality. other than 0 use interval notation to express the... (answered by jim_thompson5910)
Solve the compound inequality. Other than 0 use interval notation to express the... (answered by jim_thompson5910)
Solve the absolute value inequality. Other than , use interval notation to express the... (answered by lwsshak3)
How do I graph 4x - 5 (answered by rapaljer)
Use a number line to graph the solution set to the inequality.
xis greater than or equal (answered by ewatrrr)