Solve the equation 8x + 3 = 9x - 2x. Check the solution.
Understand the Problem
The question is asking to solve the equation 8x + 3 = 9x - 2x and then check the solution. This involves isolating the variable x and performing algebraic operations to find the value of x.
Answer
$x = -3$
Answer for screen readers
The value of $x$ is $-3$.
Steps to Solve
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Combine like terms on the right side First, simplify the right side of the equation $9x - 2x$.
This gives us:
$$ 8x + 3 = 7x $$
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Isolate the variable x To isolate $x$, subtract $7x$ from both sides:
$$ 8x - 7x + 3 = 0 $$
Simplifying further:
$$ x + 3 = 0 $$
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Solve for x Now, subtract 3 from both sides:
$$ x = -3 $$
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Check the solution Substitute $x = -3$ back into the original equation:
Left side:
$$ 8(-3) + 3 = -24 + 3 = -21 $$
Right side:
$$ 9(-3) - 2(-3) = -27 + 6 = -21 $$
Since both sides are equal, the solution is verified.
The value of $x$ is $-3$.
More Information
When solving linear equations, it’s important to perform the same operation on both sides to maintain equality. Checking the solution confirms the accuracy of our result.
Tips
- Forgetting to combine like terms before isolating the variable.
- Not checking the solution after finding a value for $x$, which can lead to errors going unnoticed.
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