1. **Stating the problem:** We have a triangle with two equal sides each measuring $x+1$ meters and a base measuring $2x-1$ meters. The perimeter of the triangle is 17 meters. 2. **Setting up the equation:** The perimeter $P$ of a triangle is the sum of all its sides. Here: $$P = (x+1) + (x+1) + (2x-1)$$ Given $P = 17$, we write: $$ (x+1) + (x+1) + (2x-1) = 17 $$ 3. **Simplifying the equation:** Combine like terms: $$ x + 1 + x + 1 + 2x - 1 = 17 $$ $$ (x + x + 2x) + (1 + 1 - 1) = 17 $$ $$ 4x + 1 = 17 $$ 4. **Solving for $x$:** Subtract 1 from both sides: $$ 4x + \cancel{1} - \cancel{1} = 17 - 1 $$ $$ 4x = 16 $$ Divide both sides by 4: $$ \frac{4x}{\cancel{4}} = \frac{16}{\cancel{4}} $$ $$ x = 4 $$ 5. **Answer:** The value of $x$ is 4. This means the two equal sides are each $4 + 1 = 5$ meters, and the base is $2(4) - 1 = 7$ meters, which sums to $5 + 5 + 7 = 17$ meters, confirming the solution.