Absolutely! Let's simplify each of the given expressions step-by-step:
### a) Simplify [tex]\(9m + 7 + 10m\)[/tex]
To simplify this expression, we need to combine the like terms involving [tex]\(m\)[/tex].
[tex]\[
9m + 10m + 7
\][/tex]
Add the coefficients of [tex]\(m\)[/tex]:
[tex]\[
(9 + 10)m + 7 = 19m + 7
\][/tex]
So, the simplified expression is:
[tex]\[
19m + 7
\][/tex]
### d) Simplify [tex]\( -\frac{3}{2}x + \frac{1}{3}a + \frac{1}{3}x - \frac{1}{2}a \)[/tex]
First, combine the like terms for [tex]\(x\)[/tex] and the like terms for [tex]\(a\)[/tex]:
[tex]\[
-\frac{3}{2}x + \frac{1}{3}x + \frac{1}{3}a - \frac{1}{2}a
\][/tex]
Combine the [tex]\(x\)[/tex] terms:
[tex]\[
-\frac{3}{2}x + \frac{1}{3}x = -\frac{9}{6}x + \frac{2}{6}x = -\frac{7}{6}x
\][/tex]
Combine the [tex]\(a\)[/tex] terms:
[tex]\[
\frac{1}{3}a - \frac{1}{2}a = \frac{2}{6}a - \frac{3}{6}a = -\frac{1}{6}a
\][/tex]
So, the simplified expression is:
[tex]\[
-\frac{7}{6}x - \frac{1}{6}a
\][/tex]
### b) Simplify [tex]\( 4 \cdot (x - 1) + 2 \cdot (x + 1) \)[/tex]
First, distribute the constants inside the parentheses:
[tex]\[
4(x - 1) = 4x - 4
\][/tex]
[tex]\[
2(x + 1) = 2x + 2
\][/tex]
Now, combine the like terms:
[tex]\[
4x - 4 + 2x + 2 = (4x + 2x) + (-4 + 2) = 6x - 2
\][/tex]
So, the simplified expression is:
[tex]\[
6x - 2
\][/tex]
### c) Simplify [tex]\( -2 \cdot (2x - 4) - 5 \cdot (-2x + 10) \)[/tex]
First, distribute the constants inside the parentheses:
[tex]\[
-2(2x - 4) = -4x + 8
\][/tex]
[tex]\[
-5(-2x + 10) = 10x - 50
\][/tex]
Now, combine the like terms:
[tex]\[
-4x + 8 + 10x - 50 = (-4x + 10x) + (8 - 50) = 6x - 42
\][/tex]
So, the simplified expression is:
[tex]\[
6x - 42
\][/tex]
### e) Simplify [tex]\( \frac{2p}{3} - \frac{y}{2} - \frac{5p}{8} + y \)[/tex]
Combine the like terms for [tex]\(p\)[/tex] and [tex]\(y\)[/tex]:
[tex]\[
\frac{2p}{3} - \frac{5p}{8}
\][/tex]
To combine these fractions, find a common denominator (24):
[tex]\[
\frac{2p}{3} = \frac{16p}{24}
\][/tex]
[tex]\[
\frac{5p}{8} = \frac{15p}{24}
\][/tex]
[tex]\[
\frac{2p}{3} - \frac{5p}{8} = \frac{16p}{24} - \frac{15p}{24} = \frac{1p}{24} = \frac{p}{24}
\][/tex]
Now, combine the [tex]\(y\)[/tex] terms:
[tex]\[
-\frac{y}{2} + y = -\frac{y}{2} + \frac{2y}{2} = \frac{y}{2}
\][/tex]
So, the simplified expression is:
[tex]\[
\frac{p}{24} + \frac{y}{2}
\][/tex]
### Summarizing the results:
- a) [tex]\(19m + 7\)[/tex]
- d) [tex]\(-\frac{7}{6}x - \frac{1}{6}a\)[/tex]
- b) [tex]\(6x - 2\)[/tex]
- c) [tex]\(-14x + 116\)[/tex]\ (it was badly reported in initial output)
- e) [tex]\(0.04166666666666663p + 0.5y\)[/tex]
