1. If x = 3, y = 2, find the value of: a) x + y b) 2x + 3y c) x^2 + y^2 2. Write algebraic expressions for the following: a) The sum of a number and 9 b) Three times a number decreased by 4 c) Half of a number increased by 7 3. Solve for x: a) x + 5 = 12 b) 3x = 18 c) x - 4 = 9
Answer (1)
Let's go through each part of the question step-by-step:
1. If x = 3 , y = 2 , find the value of:
a) x + y
To find x + y , simply add the values of x and y :
x + y = 3 + 2 = 5
b) 2 x + 3 y
First, substitute the values of x and y :
2 x + 3 y = 2 ( 3 ) + 3 ( 2 ) = 6 + 6 = 12
c) x 2 + y 2
Now, calculate the square of x and y , and then add them: x 2 + y 2 = 3 2 + 2 2 = 9 + 4 = 13
2. Write algebraic expressions for the following:
a) The sum of a number and 9
Let the number be represented by n . The expression is: n + 9
b) Three times a number decreased by 4
Again, using n as the number, the expression becomes: 3 n − 4
c) Half of a number increased by 7
Let the number be n , so the expression is: 2 n + 7
3. Solve for x :
a) x + 5 = 12
To find x , subtract 5 from both sides: x = 12 − 5 = 7
b) 3 x = 18
Divide both sides by 3 to solve for x :
x = 3 18 = 6
c) x − 4 = 9
Add 4 to both sides to find x :
x = 9 + 4 = 13
I hope this helps you understand how to tackle these types of problems! Feel free to ask if you have any more questions.
