AI Math Solver
Resources
Questions
Pricing
Login
Register
Home
>
Questions
>
Determine if 2x + 5 = 5x - 1 has no solution, one solution, or infinitely many solutions
Mathematics
Grade 8
Question Content
Tell whether the equation 2x + 5 = 5x - 1 has no solution, one solution, or infinitely many solutions.
Correct Answer
One solution: x = 2
Detailed Solution Steps
1
Step 1: Isolate the variable terms on one side. Subtract 2x from both sides: 2x - 2x + 5 = 5x - 2x - 1, which simplifies to 5 = 3x - 1.
2
Step 2: Isolate the constant terms on the other side. Add 1 to both sides: 5 + 1 = 3x - 1 + 1, which simplifies to 6 = 3x.
3
Step 3: Solve for x. Divide both sides by 3: 6/3 = 3x/3, so x = 2. Since we found a single unique value for x, the equation has one solution.
Knowledge Points Involved
1
Solving one-variable linear equations
A one-variable linear equation has the form ax + b = cx + d, where a, b, c, d are constants and x is the variable. To solve, you isolate variable terms on one side and constant terms on the other, then solve for x by performing inverse operations (addition/subtraction, multiplication/division) that maintain equality on both sides of the equation.
2
Identifying one solution for linear equations
A one-variable linear equation has one unique solution when, after simplifying, you can solve for a single value of x. This happens when the coefficients of x on both sides are different (a ≠ c in ax + b = cx + d).
Loading solution...
