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a) [tex]9m + 7 + 10m =[/tex]

b) [tex]4 \cdot (x - 1) + 2 \cdot (x + 1) =[/tex]

c) [tex]-2 \cdot (2x - 4) - 5 \cdot (-2x + 10) =[/tex]

d) [tex]-\frac{3}{2}x + \frac{1}{3}a + \frac{1}{3}x - \frac{1}{2}a =[/tex]

e) [tex]\frac{2p}{3} - \frac{y}{2} - \frac{5p}{8} + y =[/tex]



Answer :

GinnyAnswer
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]

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