Question

write an equation that says that the length of the green line is equal to the length of the black line. combine like terms. then solve for g. 49 image of green line labeled 49 and black line divided into five segments each labeled g

Explanation:

Step1: Identify the equation

The black line has 5 segments each of length \( g \), so its total length is \( 5g \). The green line has length 49. So the equation is \( 5g = 49 \)? Wait, no, wait. Wait, looking at the diagram, maybe I miscounted. Wait, the black line: let's see the marks. Wait, the black line has 5 segments? Wait, the green line is 49, and the black line is composed of 5 \( g \)? Wait, no, maybe the black line is \( 5g \) and green is 49, so equation is \( 5g = 49 \)? Wait, no, maybe I made a mistake. Wait, let's check again. The problem says "the length of the green line is equal to the length of the black line". So green line is 49, black line is \( g + g + g + g + g = 5g \)? Wait, no, wait the diagram: the black line has 5 segments? Wait, the user's diagram: the black line has 5 \( g \)s? Wait, the green line is 49. So equation is \( 5g = 49 \)? Wait, no, maybe I miscounted. Wait, maybe the black line is 5g, green is 49, so \( 5g = 49 \)? Wait, no, that can't be, because 49 divided by 5 is not integer. Wait, maybe I miscounted the number of \( g \)s. Wait, let's look again. The black line: how many \( g \) segments? Let's see the crosses: first cross after first \( g \), second after second, third after third, fourth after fourth, fifth \( g \) at the end? Wait, maybe it's 5 \( g \)s? Wait, but 5g = 49 would give g = 9.8, but maybe the diagram has 5g? Wait, no, maybe the green line is 49, and black line is 5g, so equation is \( 5g = 49 \)? Wait, no, maybe I made a mistake. Wait, perhaps the black line is 5g, so equation is \( 5g = 49 \), then solve for g: \( g = \frac{49}{5} = 9.8 \)? But that seems odd. Wait, maybe the diagram has 5 segments, but maybe I misread. Wait, the problem says "Combine like terms". Wait, maybe the black line is \( 5g \), green is 49, so equation \( 5g = 49 \). Then solve for g: divide both sides by 5: \( g = \frac{49}{5} = 9.8 \). But maybe I miscounted the number of \( g \)s. Wait, let's check the diagram again. The user's image: the black line has 5 \( g \)s (since there are 5 \( g \) labels), and green is 49. So equation is \( 5g = 49 \). Then solve for g: \( g = 49 \div 5 = 9.8 \). Wait, but maybe the diagram has 5g, so that's the equation.

Step1: Write the equation

The length of the black line is \( 5g \) (since there are 5 segments each of length \( g \)) and the length of the green line is 49. So the equation is \( 5g = 49 \).

Step2: Solve for \( g \)

To solve for \( g \), divide both sides of the equation by 5:
\( g = \frac{49}{5} = 9.8 \)

Wait, but maybe I miscounted the number of \( g \)s. Wait, let's check the diagram again. The black line: how many \( g \) segments? Let's see the marks: the first \( g \), then a cross, second \( g \), cross, third \( g \), cross, fourth \( g \), cross, fifth \( g \). So that's 5 \( g \)s. So total length of black line is \( 5g \), green is 49. So equation \( 5g = 49 \), then \( g = 49/5 = 9.8 \).

Answer:

The equation is \( 5g = 49 \) and \( g = \frac{49}{5} = 9.8 \) (or \( g = 9.8 \))