To evaluate the expression [tex]\(-2y - x\)[/tex] where [tex]\( x = \frac{3}{10} \)[/tex] and [tex]\( y = -\frac{3}{5} \)[/tex], follow these steps:
1. Substitute the given values for [tex]\( x \)[/tex] and [tex]\( y \)[/tex] into the expression:
[tex]\[
-2y - x \quad \text{becomes} \quad -2\left(-\frac{3}{5}\right) - \frac{3}{10}
\][/tex]
2. Simplify the term involving [tex]\( y \)[/tex]:
[tex]\[
-2\left(-\frac{3}{5}\right) = 2 \times \frac{3}{5} = \frac{6}{5}
\][/tex]
So now the expression is:
[tex]\[
\frac{6}{5} - \frac{3}{10}
\][/tex]
3. Find a common denominator to combine the fractions:
To subtract these fractions, we need a common denominator. The least common multiple of 5 and 10 is 10.
Convert [tex]\(\frac{6}{5}\)[/tex] to a fraction with a denominator of 10:
[tex]\[
\frac{6}{5} = \frac{6 \times 2}{5 \times 2} = \frac{12}{10}
\][/tex]
Now the expression is:
[tex]\[
\frac{12}{10} - \frac{3}{10}
\][/tex]
4. Subtract the fractions:
[tex]\[
\frac{12}{10} - \frac{3}{10} = \frac{12 - 3}{10} = \frac{9}{10}
\][/tex]
Therefore, the value of the expression [tex]\(-2y - x\)[/tex] when [tex]\( x = \frac{3}{10} \)[/tex] and [tex]\( y = -\frac{3}{5} \)[/tex] is [tex]\(\frac{9}{10}\)[/tex].
In decimal form, [tex]\(\frac{9}{10}\)[/tex] is approximately [tex]\( 0.9 \)[/tex], which matches the numerical result.
