Solve 22-8x=2x+9
Understand the Problem
The question requires solving a linear equation for the unknown variable 'x'. This involves isolating 'x' on one side of the equation by performing algebraic operations such as addition, subtraction, multiplication, and division to both sides of the equation.
Answer
$x = 11$
Answer for screen readers
$x = 11$
Steps to Solve
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Distribute on both sides of the equation Distribute the numbers outside the parentheses to the terms inside the parentheses on both sides of the equation: $3(x + 4) = 5(x - 2)$ becomes $3x + 12 = 5x - 10$
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Group the x terms on one side Subtract $3x$ from both sides of the equation to group the $x$ terms on the right side: $3x + 12 - 3x = 5x - 10 - 3x$ which simplifies to $12 = 2x - 10$
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Isolate the x term Add 10 to both sides of the equation to isolate the term with $x$: $12 + 10 = 2x - 10 + 10$ which simplifies to $22 = 2x$
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Solve for x Divide both sides of the equation by 2 to solve for $x$: $\frac{22}{2} = \frac{2x}{2}$ which simplifies to $11 = x$
$x = 11$
More Information
The solution to the equation $3(x + 4) = 5(x - 2)$ is $x = 11$. This means that when $x$ is replaced with 11 in the original equation, both sides of the equation are equal.
Tips
A common mistake is not distributing correctly in the first step, for example, forgetting to multiply both terms inside the parentheses. Another common mistake is making errors when combining like terms or not performing the same operation on both sides of the equation, which would violate the equality.
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