Solve the equation: 0.3(x-10) - 1.8 = 2.7x
Understand the Problem
The question requires solving a linear equation for the variable 'x'. This involves distributing, combining like terms, and isolating 'x' on one side of the equation.
Answer
$x = \frac{11}{3}$
Answer for screen readers
$x = \frac{11}{3}$
Steps to Solve
- Distribute on both sides of the equation
Begin by distributing the numbers outside the parentheses to the terms inside the parentheses on both sides of the equation:
$2(x + 3) = 5(x - 1)$
$2x + 6 = 5x - 5$
- Isolate the variable terms on one side
Subtract $2x$ from both sides of the equation to get all the 'x' terms on one side:
$2x + 6 - 2x = 5x - 5 - 2x$
$6 = 3x - 5$
- Isolate the constant terms on the other side
Add 5 to both sides of the equation to isolate the term with 'x':
$6 + 5 = 3x - 5 + 5$
$11 = 3x$
- Solve for x
Divide both sides by 3 to solve for 'x':
$\frac{11}{3} = \frac{3x}{3}$
$x = \frac{11}{3}$
$x = \frac{11}{3}$
More Information
The solution to the equation $2(x + 3) = 5(x - 1)$ is $x = \frac{11}{3}$. This can be expressed as an improper fraction or as a mixed number, $3\frac{2}{3}$.
Tips
A common mistake is not distributing correctly, especially with negative signs. For example, distributing the 5 on the right side of the equation to get $5x - 1$ instead of $5x - 5$. Another common mistake is making arithmetic errors when adding or subtracting terms during the isolation steps.
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