(0,7x-2,1)-(0,5-2x) =0,9(3x-1) +0,1

To solve the equation \((0.7x - 2.1) - (0.5 - 2x) = 0.9(3x - 1) + 0.1\), we will first simplify both sides step by step.

Step 1: Simplify the left side

\[ (0.7x - 2.1) - (0.5 - 2x) = 0.7x - 2.1 - 0.5 + 2x \] Combine like terms:

\[ = (0.7x + 2x) + (-2.1 - 0.5) = 2.7x - 2.6 \]

Step 2: Simplify the right side

First, simplify the expression inside the parentheses:

\[ 0.9(3x - 1) + 0.1 = 0.9 \times 3x - 0.9 \times 1 + 0.1 = 2.7x - 0.9 + 0.1 \] Combine like terms:

\[ = 2.7x - 0.8 \]

Step 3: Set the simplified sides equal to each other

Now we have:

\[ 2.7x - 2.6 = 2.7x - 0.8 \]

Step 4: Solve for x

Next, subtract \(2.7x\) from both sides:

\[ -2.6 = -0.8 \]

This statement is not true, meaning that there is no solution for \(x\). The original equation is an identity that results from parallel lines in a graph, which means the left side and the right side are equal for all \(x\) when the coefficients are the same and only the constants differ.

Conclusion:

There is no solution for the equation, meaning it holds true for all \(x\) due to the nature of the lines represented by the two sides of the equation being parallel.