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We are given a triangle where the lengths of the three sides are \( 5x \), \( 4x + 3 \), and \( x - 1 \). The perimeter of the triangle is 62 units, which means the sum of the three sides must equal 62. We can set up the following equation to solve for \( x \):

\[
5x + (4x + 3) + (x - 1) = 62
\]

Now, let's solve this equation:

\[
5x + 4x + 3 + x - 1 = 62
\]
\[
10x + 2 = 62
\]
\[
10x = 60
\]
\[
x = 6
\]

Thus, the value of \( x \) is 6.

Would you like any further details or clarification?

Here are 5 related questions you might find helpful:
1. How would the solution change if the perimeter was different?
2. Can you find the actual lengths of the sides of the triangle?
3. How would you verify that these sides form a valid triangle?
4. What is the formula for the perimeter of a polygon?
5. How do you solve perimeter problems with variables on all sides?

**Tip:** Always check if the solution for \( x \) makes sense in the context of the problem (e.g., ensuring no side has a negative length).

The perimeter of the triangle below is 62 units. Find the value of x. The sides of the triangle are labeled as 5x, 4x + 3, and x - 1.

Solve an algebraic perimeter problem where the perimeter of a triangle is 62 units. The sides are represented as 5x, 4x + 3, and x - 1. Learn how to set up and solve the equation to find the value of x. Suitable for students in Grades 7-8.

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