To solve the equation \( 4x + 5x - 8 = 1 \), we first combine like terms.
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Combine \( 4x \) and \( 5x \): \[ 4x + 5x = 9x \] So the equation becomes: \[ 9x - 8 = 1 \]
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Next, we add 8 to both sides to isolate the term with \( x \): \[ 9x - 8 + 8 = 1 + 8 \] This simplifies to: \[ 9x = 9 \]
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Now, we divide both sides by 9 to solve for \( x \): \[ x = \frac{9}{9} = 1 \]
Now let's check the solution by substituting \( x = 1 \) back into the original equation:
Substituting \( x = 1 \): \[ 4(1) + 5(1) - 8 = 1 \] Calculating the left side: \[ 4 + 5 - 8 = 1 \implies 9 - 8 = 1 \implies 1 = 1 \]
Since both sides of the equation are equal, the solution \( x = 1 \) is correct.
Thus, the solution to the equation is: \[ \boxed{1} \]