To solve the expression [tex]\(\frac{5x - 2}{3} \times (-12)\)[/tex], follow these steps:
1. Write down the original expression:
[tex]\[
\frac{(5x - 2)}{3} \times (-12)
\][/tex]
2. Multiply the entire fraction by [tex]\(-12\)[/tex]:
To multiply a fraction by a number, you multiply the numerator by that number. So we can rework the expression as follows:
[tex]\[
\left(\frac{5x - 2}{3}\right) \times (-12) = \frac{(5x - 2) \times (-12)}{3}
\][/tex]
3. Distribute [tex]\(-12\)[/tex] in the numerator:
Distribute [tex]\(-12\)[/tex] across the terms in the numerator:
[tex]\[
\frac{5x \times (-12) - 2 \times (-12)}{3}
\][/tex]
4. Perform the multiplications inside the numerator:
[tex]\[
5x \times (-12) = -60x
\][/tex]
and
[tex]\[
-2 \times (-12) = 24
\][/tex]
So the expression becomes:
[tex]\[
\frac{-60x + 24}{3}
\][/tex]
5. Simplify the fraction:
Now, we simplify each term in the numerator by dividing by the denominator (which is 3):
[tex]\[
\frac{-60x}{3} + \frac{24}{3} = -20x + 8
\][/tex]
6. Write the simplified result:
The simplified form of the expression [tex]\(\frac{5x - 2}{3} \times (-12)\)[/tex] is:
[tex]\[
8 - 20x
\][/tex]
So, the final answer to the expression [tex]\(\frac{5x - 2}{3} \times (-12)\)[/tex] is:
[tex]\[
8 - 20x
\][/tex]
