EVALUATE NON LINEAR EXPRESSIONS

Example 1 :

Evaluate the following expression for x = 3 :

2x²

Solution :

= 2x²

Substitute x = 3.

= 2(3)²

Example 2 :

Evaluate the following expression for x = 2 and y = 3 :

x² + y²

Solution :

= x² + y²

Substitute x = 2 and y = 3.

= 2² + 3²

Example 3 :

Evaluate the following expression for x = -2 :

3x³

Solution :

= 3x³

Substitute x = -2.

= 3(-2)³

Example 4 :

Evaluate the following expression for x = -1 and y = 2 :

x² + 3y³

Solution :

= x² + 3y³

Substitute x = -1 and y = 2.

= (-1)² + 3(2)²

Example 5 :

Evaluate the following expression for x = 1 and y = -2 :

3x² - 2y³

Solution :

= 3x² - 2y³

Substitute x = 1 and y = -2.

= 3(1)² - 2(-2)³

Example 6 :

Evaluate the following expression for x = 1 and y = 2 :

y² ÷ 2 + x³

Solution :

= y² ÷ 2 + x³

Substitute x = 1 and y = 2.

= 2² ÷ 2 + 1³

Example 7 :

Evaluate the following expression for x = 3 and y = -1 :

x² + y + y²

Solution :

= x² + y + y²

Substitute x = 3 and y = -1.

= 3² + (-1) + (-1)²

Example 8 :

Evaluate the following expression for x = 6, y = 8 and z = 6.

z²(x + y)

Solution :

= z²(x + y)

Substitute x = 6, y = 8 and z = 6.

= 6²(6 + 8)

Example 9 :

Evaluate the following expression for x = 1 and y = 1.

(y³ + x) ÷ 2 + x

Solution :

= (y³ + x) ÷ 2 + x

Substitute x = 1 and y = 1.

= (1³ + 1) ÷ 2 + 1

Example 10 :

Evaluate the following expression for y = 3 and z = 7.

z³ - (y ÷ 3 - 1)

Solution :

= z³ - (y ÷ 3 - 1)

Substitute y = 3 and z = 7.

= 7³ - (3 ÷ 3 - 1)

Example 11 :

You are saving for a skateboard. Your aunt gives you $45 to start and you save $3 each week.

The expression 45 + 3w gives the amount of money you save after w weeks.

a. How much will you have after 4 weeks, 10 weeks, and 20 weeks?

b. After 20 weeks, can you buy the skateboard? Explain.

Solution :

a)

Given expression is,

saving after w weeks = 45 + 3w

When w = 4

Savings after 4 weeks = 45 + 3(4)

= 45 + 12

= 57

When w = 10

Savings after 10 weeks = 45 + 3(10)

= 45 + 30

= 75

When w = 20

Savings after 20 weeks = 45 + 3(20)

= 45 + 60

= 105

b) The amount we have after 20 weeks is $105. The price of the skate board is $125. Then, the amount is not enough.

Example 12 :

Write and evaluate an expression for the problem.

a) You receive $8 for raking leaves for 2 hours. What is your hourly wage?

b)  Music lessons cost $20 per week. How much do 6 weeks of lessons cost?

c) The scores on your first two history tests were 82 and 95. By how many points did you improve on your second test?

Solution :

a)

Let x be the wage for one hour.

Amount recived for 2 x = $8

x = 8/2

Hourly wage = $4

b) 

Cost per week = 20

Number of weeks of work = 6

So, cost of lessons = 6(20)

= 120

c)

Score for first test = 82

Score for second test = 95

Points to be improved = 95 - 82

= 13

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