x = -9
5 answers
To determine if the equation \( 12 - \frac{x}{9} = 11 \) is true when \( x = -9 \), we will substitute \( x = -9 \) into the equation and simplify.
\[ 12 - \frac{-9}{9} = 11 \]
\[ \frac{-9}{9} = -1 \]
\[ 12 - (-1) = 11 \]
\[ 12 + 1 = 11 \]
\[ 13 = 11 \]
Since \( 13 \neq 11 \), the statement is false.
To solve the equation \( 12 - \frac{x}{9} = 11 \), follow these steps:
Start with the original equation:
\[ 12 - \frac{x}{9} = 11 \]
Subtract 12 from both sides:
\[ -\frac{x}{9} = 11 - 12 \]
\[ -\frac{x}{9} = -1 \]
Multiply both sides by -1 to eliminate the negative sign:
\[ \frac{x}{9} = 1 \]
Now, multiply both sides by 9:
\[ x = 9 \]
So, the solution to the equation \( 12 - \frac{x}{9} = 11 \) is
\[ \boxed{9} \]
Yes, getting rid of the negative sign (or changing the sign) is a common algebraic step used to simplify equations. It helps in making the equation easier to work with, particularly when solving for a variable.
When you have a negative term, you can multiply both sides of the equation by -1 to eliminate that negative sign. For example, in the equation:
\[ -\frac{x}{9} = -1 \]
By multiplying both sides by -1, you get:
\[ \frac{x}{9} = 1 \]
This step is perfectly valid and does not change the equality of the equation because whatever you do to one side of the equation, you must do to the other side as well.
However, if you prefer not to multiply by -1, you could simply leave the equation as:
\[ -\frac{x}{9} = -1 \]
and then multiply both sides by -1 only when you solve for \(x\).
In summary, while getting rid of the negative sign is a common practice to simplify the process, it is not mandatory, and you can use different methods to reach the same solution. It’s all about what you find more intuitive and straightforward.
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