Math Problem Statement

Jubal wrote the four equations below. He examined them, without solving them, to determine which equation has no solution.

Which of Jubal’s equations has no solution? 7x+1=7x+1, 3x+2=3x-2, 4x+1=3x+8, -2x-1=-2x-1,

Solution

To determine which of Jubal's equations has no solution, we can analyze each equation.

  1. Equation: 7x+1=7x+17x + 1 = 7x + 1
    Simplifying, we subtract 7x7x from both sides:
    1=11 = 1
    This is always true, so this equation has infinitely many solutions.

  2. Equation: 3x+2=3x23x + 2 = 3x - 2
    Simplifying, we subtract 3x3x from both sides:
    2=22 = -2
    This is never true, so this equation has no solution.

  3. Equation: 4x+1=3x+84x + 1 = 3x + 8
    Simplifying, we subtract 3x3x from both sides:
    x+1=8x + 1 = 8
    Subtracting 1 from both sides gives:
    x=7x = 7
    This equation has a single solution x=7x = 7.

  4. Equation: 2x1=2x1-2x - 1 = -2x - 1
    Simplifying, we add 2x2x to both sides:
    1=1-1 = -1
    This is always true, so this equation has infinitely many solutions.

Conclusion: The equation that has no solution is 3x+2=3x23x + 2 = 3x - 2.

Would you like more details or have any other questions?

Here are 5 related questions:

  1. What does it mean for an equation to have no solution?
  2. How do you determine if an equation has infinitely many solutions?
  3. Can an equation have exactly two solutions? Why or why not?
  4. What are the steps to solve a linear equation?
  5. What is the difference between a consistent and inconsistent system of equations?

Tip: When comparing both sides of an equation, if the variables cancel out and you end up with a false statement (like 2=22 = -2), the equation has no solution.

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Math Problem Analysis

Mathematical Concepts

Equations
Solution analysis
Infinite solutions
No solution

Formulas

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Theorems

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Suitable Grade Level

High school