Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Q8) Simplify the following:

i. [tex]\(5a + 3b + 2a + b = \qquad\)[/tex]

ii. [tex]\(7p + 4q - 2p + q = \qquad\)[/tex]

iii. [tex]\(2x + 4y - 5y = \qquad\)[/tex]

iv. [tex]\(5x + 22 - 7x - 27 = \qquad\)[/tex]

v. [tex]\(\frac{1}{2}x + \frac{1}{4}x = \qquad\)[/tex]

Sagot :

GinnyAnswer
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]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.