AI Math Solver
Resources
Questions
Pricing
Login
Register
Home
>
Questions
>
Determine if 7x - 1 = 4x + 8 has no solution, one solution, or infinitely many solutions
Mathematics
Grade 8
Question Content
Tell whether the equation 7x - 1 = 4x + 8 has no solution, one solution, or infinitely many solutions.
Correct Answer
One solution: x = 3
Detailed Solution Steps
1
Step 1: Isolate variable terms by subtracting 4x from both sides: 7x - 4x - 1 = 4x - 4x + 8, which simplifies to 3x - 1 = 8.
2
Step 2: Isolate constant terms by adding 1 to both sides: 3x - 1 + 1 = 8 + 1, which simplifies to 3x = 9.
3
Step 3: Solve for x by dividing both sides by 3: 3x/3 = 9/3, so x = 3. 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...
