Alright, let's simplify each provided expression step by step:
a. Simplify [tex]\(3y + 3(y - 2.5)\)[/tex]:
1. Distribute the [tex]\(3\)[/tex] to both terms inside the parentheses:
[tex]\[
3y + 3(y) - 3(2.5)
\][/tex]
2. This becomes:
[tex]\[
3y + 3y - 7.5
\][/tex]
3. Combine the like terms ([tex]\(3y\)[/tex] and [tex]\(3y\)[/tex]):
[tex]\[
6y - 7.5
\][/tex]
So, the simplified expression is:
[tex]\[
6y - 7.5
\][/tex]
b. Simplify [tex]\(6.25m + 9 + 3.75m - 12\)[/tex]:
1. Combine the like terms ([tex]\(6.25m\)[/tex] and [tex]\(3.75m\)[/tex]):
[tex]\[
(6.25 + 3.75)m + 9 - 12
\][/tex]
[tex]\[
10m + 9 - 12
\][/tex]
2. Combine the constants ([tex]\(9\)[/tex] and [tex]\(-12\)[/tex]):
[tex]\[
10m - 3
\][/tex]
So, the simplified expression is:
[tex]\[
10m - 3
\][/tex]
c. Simplify [tex]\(4.5a + 7 + 3.5a + 2\)[/tex]:
1. Combine the like terms ([tex]\(4.5a\)[/tex] and [tex]\(3.5a\)[/tex]):
[tex]\[
(4.5 + 3.5)a + 7 + 2
\][/tex]
[tex]\[
8a + 7 + 2
\][/tex]
2. Combine the constants ([tex]\(7\)[/tex] and [tex]\(2\)[/tex]):
[tex]\[
8a + 9
\][/tex]
So, the simplified expression is:
[tex]\[
8a + 9
\][/tex]
d. Simplify [tex]\(0.5(-12p - 4)\)[/tex]:
1. Distribute the [tex]\(0.5\)[/tex] to both terms inside the parentheses:
[tex]\[
0.5(-12p) + 0.5(-4)
\][/tex]
2. This becomes:
[tex]\[
-6p - 2
\][/tex]
So, the simplified expression is:
[tex]\[
-6p - 2
\][/tex]
e. Simplify [tex]\(-6\left(m + \frac{1}{2}\right)\)[/tex]:
1. Distribute the [tex]\(-6\)[/tex] to both terms inside the parentheses:
[tex]\[
-6(m) + -6\left(\frac{1}{2}\right)
\][/tex]
2. This becomes:
[tex]\[
-6m - 3
\][/tex]
So, the simplified expression is:
[tex]\[
-6m - 3
\][/tex]
f. Simplify [tex]\(7(y + 7) - 11y\)[/tex]:
1. Distribute the [tex]\(7\)[/tex] to both terms inside the parentheses:
[tex]\[
7(y) + 7(7) - 11y
\][/tex]
2. This becomes:
[tex]\[
7y + 49 - 11y
\][/tex]
3. Combine the like terms ([tex]\(7y\)[/tex] and [tex]\(-11y\)[/tex]):
[tex]\[
(7 - 11)y + 49
\][/tex]
[tex]\[
-4y + 49
\][/tex]
So, the simplified expression is:
[tex]\[
-4y + 49
\][/tex]
