0,1y/12-0,3y+2/12>-1/4
To solve the inequality \(\frac{0.1y}{12} - 0.3y + \frac{2}{12} > -\frac{1}{4}\), we can follow these steps:
Convert everything to a common denominator to make it easier to work with the fractions. The common denominator for 12 and 4 is 12. Thus, we can rewrite \(-\frac{1}{4}\) as \(-\frac{3}{12}\):
\[ \frac{0.1y}{12} - 0.3y + \frac{2}{12} > -\frac{3}{12} \]
Combine like terms: We will first convert \(-0.3y\) into a fraction with a denominator of 12.
\(-0.3y = -\frac{3y}{10}\). We need to find a common denominator for this term as well to facilitate combination. We will express \(y\) in terms of 12:
\[ -0.3y = -\frac{3y \cdot 12}{10 \cdot 12} = -\frac{36y}{120} \]
However, for simplicity, let's revert back to the original forms and combine entire inequality from step 1.
To proceed with combining fractions, first combine \(\frac{0.1y}{12}\) and \(\frac{2}{12}\):
\[ \frac{0.1y + 2}{12} > -\frac{3}{12} \]
Multiply through by 12 to eliminate the denominator. Since we’re multiplying by a positive number, the inequality direction remains the same.
\[ 0.1y + 2 > -3 \]
Isolate \(y\): Subtract \(2\) from both sides:
\[ 0.1y > -3 - 2 \]
\[ 0.1y > -5 \]
Divide both sides by \(0.1\) (which is positive, so the inequality does not change):
\[ y > -5 \div 0.1 \]
\[ y > -50 \]
So, the solution to the inequality is:
\[ y > -50 \]
This means that \(y\) can take any value greater than \(-50\).
