Question

Point T is between points E and M.The points are collinear.

EM = 4x - 5
ET = x + 1
TM = 9
EM⁻ =?

Answer 1

To find the length of segment EM, we use the given algebraic expressions for the lengths of segments ET, TM, and EM. After solving the equations, we conclude that the length of segment EM is 15 units.

Step-by-step explanation:

The student's question involves solving an algebraic equation to find the length of a segment within a line. Given that points T, E, and M are collinear, with T between E and M, and that the lengths of the segments are represented by algebraic expressions (EM = 4x - 5, ET = x + 1, TM = 9), we want to find EM by setting up the equation ET + TM = EM to solve for x.

First, we substitute the expressions for ET and TM into the equation:
(x + 1) + 9 = 4x - 5.

Next, we solve for x:

1. Combine like terms on both sides: x + 10 = 4x - 5.
2. Subtract x from both sides: 10 = 3x - 5.
3. Add 5 to both sides: 15 = 3x.
4. Divide by 3: x = 5.

Now, with the value of x, we can find EM by substituting x into the given expression:

EM = 4(5) - 5 = 20 - 5 = 15.

Therefore, the length of EM is 15 units.