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Solve for [tex]\( x \)[/tex].

[tex]\[ 3x = 6x - 2 \][/tex]



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8.10/A rope is remaining length [tex]$(8 x+7) cm$[/tex]. If a length of [tex]$(2 x+4) cm$[/tex] is cut for use, what is the longithenth of each side of the triangle formed?
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Response:
8.10 A rope has a remaining length of [tex]\((8x + 7) \, \text{cm}\)[/tex]. If a length of [tex]\((2x + 4) \, \text{cm}\)[/tex] is cut for use, what is the length of each side of the triangle formed?



Answer :

GinnyAnswer
Let's solve the problem step-by-step:

1. Determine the initial length of the rope:

Given the remaining length of the rope before any cut is made, we have:
[tex]\[ 8x + 7 \text{ cm} \][/tex]

2. Calculate the length of the rope that is cut:

The length of the rope cut for use is:
[tex]\[ 2x + 4 \text{ cm} \][/tex]

3. Compute the remaining length of the rope after the cut:

Subtract the cut length from the initial length to find the remaining length of the rope:
[tex]\[ \text{Remaining length after cut} = (8x + 7) - (2x + 4) \][/tex]

Simplify the expression:
[tex]\[ \text{Remaining length after cut} = 8x + 7 - 2x - 4 = 6x + 3 \][/tex]

4. Form a triangle with the remaining rope:

When the remaining rope is used to form a triangle with three equal sides, each side of the triangle will be:
[tex]\[ \text{Length of each side} = \frac{\text{Remaining length after cut}}{3} \][/tex]

Substitute the remaining length after the cut:
[tex]\[ \text{Length of each side} = \frac{6x + 3}{3} \][/tex]

5. Simplify the length of each side:
[tex]\[ \text{Length of each side} = \frac{6x}{3} + \frac{3}{3} = 2x + 1 \text{ cm} \][/tex]

So, the length of each side of the triangle formed is:
[tex]\[ 2x + 1 \text{ cm} \][/tex]