Let's solve the given expression step-by-step: [tex]\( 2.4(3 - x) - 0.6(2x - 3) \)[/tex].
1. Distribute the constants inside the parentheses:
a. Distribute [tex]\( 2.4 \)[/tex] across [tex]\( (3 - x) \)[/tex]:
[tex]\[
2.4 \cdot 3 - 2.4 \cdot x = 7.2 - 2.4x
\][/tex]
b. Distribute [tex]\( -0.6 \)[/tex] across [tex]\( (2x - 3) \)[/tex]:
[tex]\[
-0.6 \cdot 2x - (-0.6 \cdot 3) = -1.2x + 1.8
\][/tex]
2. Combine the two results from the distribution:
[tex]\[
7.2 - 2.4x - 1.2x + 1.8
\][/tex]
3. Combine like terms:
a. Combine the constant terms:
[tex]\[
7.2 + 1.8 = 9
\][/tex]
b. Combine the [tex]\( x \)[/tex]-terms:
[tex]\[
-2.4x - 1.2x = -3.6x
\][/tex]
4. Write the simplified expression:
[tex]\[
9 - 3.6x
\][/tex]
So, the simplified form of the given expression [tex]\( 2.4(3 - x) - 0.6(2x - 3) \)[/tex] is:
[tex]\[
9 - 3.6x
\][/tex]
