how many solutions are there to the equation below?
6x+30+4x=10(x+3)
I want to know how to do this problems
Please and Thank you
10 x + 30 = 10 x + 30
ANY value of x works
INFINITE number of solutions
BUT
what if it were
10 x + 30 = 10 x + 40
then there would be no solutions at all
To solve the equation 6x + 30 + 4x = 10(x + 3), you can follow these steps:
Step 1: Distribute the 10 to the terms inside the parentheses:
6x + 30 + 4x = 10x + 30
Step 2: Combine like terms on both sides of the equation:
6x + 4x - 10x = 30 - 30
0 = 0
Step 3: Simplify both sides of the equation.
No matter what value x takes, both sides of the equation will always be equal to 0.
Step 4: Determine the number of solutions.
Since both sides of the equation are always equal, this equation has an infinite number of solutions.
Therefore, there are infinitely many solutions to the equation 6x + 30 + 4x = 10(x + 3).
To find the number of solutions to the equation 6x + 30 + 4x = 10(x + 3), we need to simplify the equation and then determine its nature.
Step 1: Simplify the equation
Start by distributing the 10 to both terms inside the parentheses on the right side:
6x + 30 + 4x = 10x + 30
Step 2: Combine like terms
Combine the x terms on the left side:
10x + 30 = 10x + 30
Step 3: Move all x terms to one side
To do this, subtract 10x from both sides:
10x - 10x +30 = 10x - 10x + 30
This simplifies to:
30 = 30
Step 4: Evaluate the result
After simplifying the equation, we get 30 = 30. This equation is a tautology, meaning it is always true, regardless of the value of x.
Therefore, this equation has infinitely many solutions.