How many solutions can be found for the linear equation?
(15x+21)/3 = 5x +7
no solution
one solution
two solutions
infinitely many solutions
one solution
To determine the number of solutions for the given linear equation, we can simplify the equation and compare the coefficients of the variables.
Start by simplifying the equation:
(15x+21)/3 = 5x + 7
Divide both sides of the equation by 3 to eliminate the fraction:
(15x+21)/3 = (5x+7)
(5x+7) = 5x + 7
Now, we can see that the equation simplifies to a statement that is always true:
5x + 7 = 5x + 7
This means that the equation has infinitely many solutions.
Therefore, the correct answer is: Infinitely many solutions.
To determine how many solutions can be found for the linear equation, we need to solve the equation and analyze the results.
Let's first simplify the equation:
(15x + 21)/3 = 5x + 7
By multiplying both sides of the equation by 3, we can eliminate the denominator:
15x + 21 = 15x + 21
Now, if we subtract 15x from both sides, we get:
21 = 21
At this point, we notice that the variable "x" has been eliminated. We are left with the equation 21 = 21.
This equation is a true statement, meaning that both sides are equal. Thus, every value of "x" will satisfy the equation.
In summary, there are infinitely many solutions for this linear equation.