Exercise 1: Write algebraic expressions for the following statements, making the unknown x. 1. The sum of an unknown number and 7. 2. The product of an unknown number and 3. 3. The difference between a certain number and 8. 4. Two more than double a number. Exercise 2: 1. If A = 3x² + 5x - 2; B = -2x - x² + 7; C = -5 + 2x² + x, determine the following: 1.1 A + C 1.2 C - B 1.3 The product of A and -2 2. Consider the following expressions: A: 3x² - 2 + 4x B: 2x - 6x² + 5x² C: 4 - 2x² + 3x 2.1 Determine the value of A + B + C 2.2 Determine -3A

Let's solve the exercises one by one.
Exercise 1 :

The sum of an unknown number and 7 :
The algebraic expression for the sum of a number x and 7 is written as:
x + 7

The product of an unknown number and 3 :
The algebraic expression for the product of a number x and 3 is written as:
3 x

The difference between a certain number and 8 :
The algebraic expression for the difference between a number x and 8 is:
x − 8

Two more than double a number :
First, double the number x to get 2 x . Then, add 2:
2 x + 2


Exercise 2 :

Expressions :

A = 3 x 2 + 5 x − 2
B = − 2 x − x 2 + 7
C = − 5 + 2 x 2 + x

1.1 A + C :
Add expressions A and C :
A + C = ( 3 x 2 + 5 x − 2 ) + ( − 5 + 2 x 2 + x )
Combine like terms:
( 3 x 2 + 2 x 2 ) + ( 5 x + x ) + ( − 2 − 5 ) = 5 x 2 + 6 x − 7
1.2 C - B :
Subtract B from C :
C − B = ( − 5 + 2 x 2 + x ) − ( − 2 x − x 2 + 7 )
Simplify and combine like terms:
( 2 x 2 + x + 2 x 2 ) + ( x + 2 x ) + ( − 5 − 7 ) = 3 x 2 + 3 x − 12
1.3 The product of A and -2 :
Multiply A by − 2 :
− 2 ( 3 x 2 + 5 x − 2 ) = − 6 x 2 − 10 x + 4

Consider the expressions :

A = 3 x 2 − 2 + 4 x
B = 2 x − 6 x 2 + 5 x 2
C = 4 − 2 x 2 + 3 x

2.1 A + B + C :
Combine all expressions:
( 3 x 2 − 2 + 4 x ) + ( 2 x − 6 x 2 + 5 x 2 ) + ( 4 − 2 x 2 + 3 x )
Combine like terms:
( 3 x 2 − 6 x 2 + 5 x 2 − 2 x 2 ) + ( 4 x + 2 x + 3 x ) + ( − 2 + 4 ) = 0 x 2 + 9 x + 2
2.2 -3A :
Multiply A by − 3 :
− 3 ( 3 x 2 − 2 + 4 x ) = − 9 x 2 + 6 − 12 x


These solutions encapsulate the algebraic manipulations required for each exercise, and each step is detailed to ensure clarity and understanding.

Answered by EmmaGraceJohnson | 2025-07-22