In solving the algebraic equation
2(x - 5) = 2x + 10, you end up with -10 = 10 what does this mean.
Slope intercept form of the equation of a straight line is:
y = m x + b
where m is the slope of the line
b is the y-intercept
The lines are parallel if their slopes are equal.
In this case:
y = 2 ( x - 5 ) = 2 x - 10
slope
m = 2
y = 2 x + 10
slope
m = 2
Since parallel lines never cross, then there can be no intersection.
That is for a system of equations that graphs as parallel lines, there can be no solution.
This is called an "inconsistent" system of equations.
There are no pairs of numbers that work in both equations.
Thank you!
It seems that there might have been a mistake in solving the equation. Let's go step-by-step to solve the equation correctly:
1. Distribute the 2 to the terms inside the parentheses:
2(x - 5) = 2x + 10
2x - 10 = 2x + 10
2. Simplify the equation by combining like terms:
2x - 10 = 2x + 10
3. Subtract 2x from both sides of the equation to isolate the variable:
2x - 2x - 10 = 2x - 2x + 10
-10 = 10
After following these steps, we end up with -10 = 10, which is not a true statement. This means that the equation 2(x - 5) = 2x + 10 has no solution. The equation is inconsistent, indicating that there are no values of x that satisfy the equation. Therefore, the original equation has no solution.
When you solve the equation 2(x - 5) = 2x + 10 and obtain -10 = 10, it means that the equation has no solution. This result is known as a contradiction.
To understand why this is the case, let's go step by step through the solution process:
Starting with the original equation: 2(x - 5) = 2x + 10
Expanding the brackets: 2x - 10 = 2x + 10
Next, let's isolate the variable x. Subtracting 2x from both sides of the equation: -10 = 10
The equation simplifies to -10 = 10, which is a false statement. This means that there is no value of x that satisfies the equation.
In other words, no matter what value of x you substitute into the equation, the left side will never equal the right side. Therefore, we say that the equation has no solution.