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Compare and Contrast: Two equations are listed below. Solve each equation and compare the solutions.

Equation 1: 15x−61=−41
Equation 2: 17x+13=127

Option A: Equation 1 and Equation 2 have the same number of solutions.
Option B: The number of solutions cannot be determined.
Option C: Equation 2 has more solutions than Equation 1.
Option D: Equation 1 has more solutions than Equation 2.

1 Answer

2 votes

Final answer:

The correct answer is option A: Both Equation 1 and Equation 2 have exactly one solution when solved. Equation 1 simplifies to x = 4/3, and Equation 2 simplifies to x = 6.71, demonstrating that each linear equation has a unique solution.

Step-by-step explanation:

The correct answer is option A: Equation 1 and Equation 2 have the same number of solutions. Both equations given are linear equations, meaning they will each have exactly one solution.

Let's solve Equation 1: 15x - 61 = -41. To find the value of x, we add 61 to both sides of the equation, getting 15x = 20. Then we divide both sides by 15 to solve for x, resulting in x = 20/15, which simplifies to x = 4/3, or approximately 1.333.

Now let's solve Equation 2: 17x + 13 = 127. We subtract 13 from both sides to get 17x = 114. We then divide both sides by 17, resulting in x = 114/17, which simplifies to x = 6.71.

Therefore, Equation 1 and Equation 2 each have one unique solution.

To solve Equation 1, you can start by adding 61 to both sides of the equation to isolate the variable: 15x = -41 + 61, which simplifies to 15x = 20. Then, divide both sides of the equation by 15 to solve for x: x = 20/15, or x = 4/3.

To solve Equation 2, start by subtracting 13 from both sides of the equation: 17x = 127 - 13, which simplifies to 17x = 114. Then, divide both sides of the equation by 17 to solve for x: x = 114/17.

Comparing the solutions, Equation 1 has a solution of x = 4/3, while Equation 2 has a solution of x = 6. Since the two equations have different solutions, the number of solutions cannot be determined.

User Rick Giuly
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