Question

Point T is on line segment start overline, S, U, end overline

SU
. Given S, U, equals, 4, x, plus, 1, commaSU=4x+1, T, U, equals, 3, x, commaTU=3x, and S, T, equals, 3, x, minus, 1, commaST=3x−1, determine the numerical length of start overline, S, U, end overline, .
SU
.

Answer 1

The length of line segment SU is found by setting up the equation (3x - 1) + (3x) = (4x + 1) and solving for x, which results in x = 1. Plugging x back into SU's equation yields SU = 4x + 1, which calculates to a length of 5 units.

Step-by-step explanation:

The student is asked to find the numerical length of line segment \( SU \). To solve this problem, we can use the property that the sum of the lengths of segments \( ST \) and \( TU \) is equal to the length of \( SU \). Therefore, we can set up the equation \( ST + TU = SU \), which translates to \( (3x - 1) + (3x) = (4x + 1) \). Simplifying this equation will allow us to solve for x, and subsequently, we can find the length of \( SU \).

Combining like terms gives us \( 3x - 1 + 3x = 4x + 1 \), which simplifies to \( 6x - 1 = 4x + 1 \). Solving for x, we get:

• Subtract 4x from both sides: \( 2x - 1 = 1 \)
• Add 1 to both sides: \( 2x = 2 \)
• Divide both sides by 2: \( x = 1 \)

Now that we have the value for x, we can plug it back into the original equation for \( SU \) to find its length:

\( SU = 4x + 1 \)
\( SU = 4(1) + 1 \)
\( SU = 4 + 1 \)
\( SU = 5 \)

Therefore, the numerical length of \( SU \) is 5 units.