Question

a*———1———•b———3x+7———•o 6x + 42 find bo. figure is not drawn to scale.

Explanation:

Step1: Assume AB + BC = AC

From the figure, AB = 1 (wait, maybe it's a typo? Wait, the total length AC is 8x - 42? Wait, no, looking at the problem again, maybe AB is a segment, BC is 3x + 7, and AC is 8x - 42? Wait, maybe the first segment is AB with length... Wait, maybe the problem is that A to B is some length, B to C is 3x + 7, and A to C is 8x - 42? Wait, maybe the first part is a typo, maybe AB is x? Wait, no, the user's image: "A---1---B---3x+7---C" and the total length A to C is 8x - 42? Wait, maybe AB is 1? No, that doesn't make sense. Wait, maybe the correct equation is AB + BC = AC. Let's assume that AB is x? Wait, no, the original problem: maybe the first segment is AB with length (maybe a typo, maybe AB is x, but in the image, it's "A---1---B---3x+7---C" and the total is 8x - 42? Wait, no, perhaps the total length AC is 8x - 42, and AB + BC = AC. So AB + (3x + 7) = 8x - 42. Wait, but AB is labeled as 1? No, that can't be. Wait, maybe it's a typo, and AB is x? Wait, no, the user's image: "A---1---B---3x+7---C" and the total length A to C is 8x - 42? Wait, maybe the 1 is a typo, and it's x. Wait, no, let's re-express. Let's suppose that the length from A to B is some value, B to C is 3x + 7, and A to C is 8x - 42. So AB + BC = AC. So if AB is, say, x, but in the image, it's "1" between A and B. Wait, maybe the problem is: A---B---C, with AB = x (but in the image, it's 1), BC = 3x + 7, and AC = 8x - 42. Wait, maybe the 1 is a typo, and it's x. Wait, no, let's check the equation. Let's assume that AB + BC = AC. So AB + (3x + 7) = 8x - 42. If AB is 1, then 1 + 3x + 7 = 8x - 42. Then 3x + 8 = 8x - 42. Subtract 3x: 8 = 5x - 42. Add 42: 50 = 5x. So x = 10. Then BC is 3x + 7 = 3*10 + 7 = 37. Wait, but let's verify. If x=10, then AC is 8x - 42 = 80 - 42 = 38. But AB + BC = 1 + 37 = 38. Yes, that works. So maybe AB is 1. So let's do that.

Step1: Set up the equation AB + BC = AC

AB is 1, BC is 3x + 7, AC is 8x - 42. So:
$$1 + (3x + 7) = 8x - 42$$

Step2: Simplify left side

Combine like terms:
$$3x + 8 = 8x - 42$$

Step3: Subtract 3x from both sides

$$8 = 5x - 42$$

Step4: Add 42 to both sides

$$50 = 5x$$

Step5: Divide both sides by 5

$$x = 10$$

Step6: Find BC

BC is 3x + 7. Substitute x=10:
$$3(10) + 7 = 30 + 7 = 37$$

Answer:

37