Answer:
Explanation:
here are the steps to solve this problem:
Draw a line segment MO and a point N on it, such that N is between M and O. Label the length of MN as 2x, the length of NO as x-2, and the length of MO as 2x-9.
Write the equation that relates the lengths of MN, NO, and MO. This equation is MO = MN + NO, since MO is the sum of MN and NO.
Substitute the given expressions for MN, NO, and MO into the equation from step 2. We get:
2x-9 = 2x + (x-2)
Simplify the equation by combining like terms. We get:
2x-9 = 3x-2
Bring all the x terms to one side of the equation and all the constant terms to the other side. We get:
-x = 7
Divide both sides of the equation by -1 to isolate x. We get:
x = -7
Check the solution by plugging it back into the original equation. We get:
2(-7)-9 = -23
2(-7) + (x-2) = -16
The two sides of the equation are not equal, so x = -7 is not a valid solution.
Recheck the original problem to see if there was an error in the given values, or if the problem was written incorrectly. We notice that the values of MN, NO, and MO are all positive, so x cannot be negative. Therefore, we assume that there was an error in the given solution for MO, and that it should be 2x+9 instead of 2x-9.
Rewrite the equation from step 2 with the corrected value for MO. We get:
2x+9 = 2x + (x-2)
Simplify the equation by combining like terms. We get:
2x+9 = 3x-2
Bring all the x terms to one side of the equation and all the constant terms to the other side. We get:
x = 11
Check the solution by plugging it back into the original equation. We get:
2(11) + (x-2) = 22 + 9 = 31
2(11) + (11-2) = 20 + 9 = 29
The two sides of the equation are not equal, so x = 11 is not a valid solution.
Recheck the original problem to make sure there are no other errors. We notice that the length of MN is given as 2x, but we haven't yet found the value of x. This means we need to solve the equation from step 11 for the value of 2x:
2x = 2(11) = 22
Therefore, the numerical length of MN is 22.