Final answer:
To find the length of segment BL, the expressions representing the lengths BL (4x + 12) and LT (3x + 11) are added together and set equal to the total length BT (58). Solving for x yields 5, which is then substituted back into the expression for BL to find the length of 32 units.
Step-by-step explanation:
The student is given a segment BT and a point L which lies between B and T, creating two segments BL and LT such that the entire length of BT equals 58 units. The lengths of BL and LT are given by expressions involving x, specifically 4x + 12 and 3x + 11 respectively. To find the length of BL, we need to create an equation that represents the sum of BL and LT being equal to the total length BT.
Setting up the equation based on the information provided:
- BL + LT = BT
- (4x + 12) + (3x + 11) = 58
- 7x + 23 = 58
- 7x = 58 - 23
- 7x = 35
- x = 5
Now that we have the value of x, we can find BL:
- BL = 4x + 12
- BL = 4(5) + 12
- BL = 20 + 12
- BL = 32
Therefore, the length of segment BL is 32 units.