Solve for x: 2x - 5 + 8x = 6x + 7
Understand the Problem
The question is asking to solve a linear equation for the variable x. The equation needs to be simplified and rearranged to find the value of x.
Answer
The value of \( x \) is \( 3 \).
Answer for screen readers
The final answer is ( x = 3 ).
Steps to Solve
- Combine Like Terms on the Left Side
Start by combining the terms involving $x$ on the left side.
$$ 2x + 8x - 5 = 10x - 5 $$
So the equation now is:
$$ 10x - 5 = 6x + 7 $$
- Isolate the Terms Involving x
Next, move the $6x$ from the right side to the left side of the equation by subtracting $6x$ from both sides.
$$ 10x - 6x - 5 = 7 $$
This simplifies to:
$$ 4x - 5 = 7 $$
- Eliminate the Constant Term
Now, add 5 to both sides to isolate the term with $x$.
$$ 4x - 5 + 5 = 7 + 5 $$
This simplifies to:
$$ 4x = 12 $$
- Solve for x
Finally, divide both sides by 4 to solve for $x$.
$$ x = \frac{12}{4} $$
So,
$$ x = 3 $$
The final answer is ( x = 3 ).
More Information
This problem showcases the basics of solving linear equations by combining like terms, isolating variables, and performing basic arithmetic operations. Understanding these steps helps in tackling more complex equations in algebra.
Tips
- Forgetting to combine like terms correctly.
- Skipping signs when moving terms from one side of the equation to another. Always double-check the signs (+ or -) when rearranging the equation.
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