Sure, let's simplify each expression step by step.
### 1. Simplify [tex]\(5a + 3b + 2a + b\)[/tex]:
We group the terms with [tex]\(a\)[/tex] and [tex]\(b\)[/tex] separately:
[tex]\[ (5a + 2a) + (3b + b) \][/tex]
Simplify the grouped terms:
[tex]\[ 7a + 4b \][/tex]
So, the simplified form of [tex]\(5a + 3b + 2a + b\)[/tex] is:
[tex]\[ 7a + 4b \][/tex]
### ii. Simplify [tex]\(7p + 4q - 2p + q\)[/tex]:
Again, group the terms with [tex]\(p\)[/tex] and [tex]\(q\)[/tex] separately:
[tex]\[ (7p - 2p) + (4q + q) \][/tex]
Simplify the grouped terms:
[tex]\[ 5p + 5q \][/tex]
So, the simplified form of [tex]\(7p + 4q - 2p + q\)[/tex] is:
[tex]\[ 5p + 5q \][/tex]
### iii. Simplify [tex]\(2x + 4y - 5y\)[/tex]:
Group the terms with [tex]\(y\)[/tex] together:
[tex]\[ 2x + (4y - 5y) \][/tex]
Simplify the grouped terms:
[tex]\[ 2x + (-1y) \][/tex]
As a convention, we can rewrite [tex]\(-1y\)[/tex] as [tex]\(-y\)[/tex]:
[tex]\[ 2x - y \][/tex]
So, the simplified form of [tex]\(2x + 4y - 5y\)[/tex] is:
[tex]\[ 2x - y \][/tex]
### iv. Simplify [tex]\(5x + 22 - 7x - 27\)[/tex]:
Group the terms with [tex]\(x\)[/tex] and the constants separately:
[tex]\[ (5x - 7x) + (22 - 27) \][/tex]
Simplify the grouped terms:
[tex]\[ -2x + (-5) \][/tex]
As a convention, we can rewrite [tex]\(-5\)[/tex] as just [tex]\(-5\)[/tex]:
[tex]\[ -2x - 5 \][/tex]
So, the simplified form of [tex]\(5x + 22 - 7x - 27\)[/tex] is:
[tex]\[ -2x - 5 \][/tex]
### v. Simplify [tex]\(\frac{1}{2}x + \frac{1}{4}x\)[/tex]:
Find a common denominator for the fractions:
[tex]\[ \frac{2}{4}x + \frac{1}{4}x \][/tex]
Add the fractions:
[tex]\[ \frac{2 + 1}{4}x \][/tex]
[tex]\[ \frac{3}{4}x \][/tex]
So, the simplified form of [tex]\(\frac{1}{2}x + \frac{1}{4}x\)[/tex] is:
[tex]\[ 0.75x \][/tex]
To summarize, here are the simplified forms of the given expressions:
1. [tex]\(5a + 3b + 2a + b = 7a + 4b\)[/tex]
ii. [tex]\(7p + 4q - 2p + q = 5p + 5q\)[/tex]
iii. [tex]\(2x + 4y - 5y = 2x - y\)[/tex]
iv. [tex]\(5x + 22 - 7x - 27 = -2x - 5\)[/tex]
v. [tex]\(\frac{1}{2}x + \frac{1}{4}x = 0.75x\)[/tex]
