Solve the Linear Equation: 5(0.4x - 0.3) + (0.8 - 0.6x) = 1.4x - 0.7
In this article, we will solve a linear equation that involves parentheses and decimals. The equation is:
5(0.4x - 0.3) + (0.8 - 0.6x) = 1.4x - 0.7
To solve this equation, we need to follow the order of operations (PEMDAS) and simplify the equation step by step.
Step 1: Simplify the Left Side of the Equation
First, let's simplify the left side of the equation by evaluating the expressions inside the parentheses:
5(0.4x - 0.3) = 5(0.4x) - 5(0.3) = 2x - 1.5
(0.8 - 0.6x) = 0.8 - 0.6x
Now, combine the two expressions:
2x - 1.5 + 0.8 - 0.6x = ?
Step 2: Combine Like Terms
Combine like terms on the left side of the equation:
2x - 1.5 + 0.8 - 0.6x = 2x - 0.6x - 1.5 + 0.8 = 1.4x - 0.7
Step 3: Equate the Expressions
Now, equate the simplified left side of the equation with the right side:
1.4x - 0.7 = 1.4x - 0.7
The equation is true for all values of x, which means it is an identity.
Conclusion
In this article, we solved the linear equation 5(0.4x - 0.3) + (0.8 - 0.6x) = 1.4x - 0.7 by simplifying the equation step by step and combining like terms. The final result shows that the equation is an identity, which means it is true for all values of x.
