You’ll be able to consider algebraic expressions while you substitute numbers for the variables within the algebraic expressions after which comply with the order of operations.

Extra examples displaying how one can consider algebraic expressions with out exponents

Instance #1

Consider 2a + b + 1 for a = 3 and b = 5

Substitute 3 for a and 5 for b

2a + b + 1 = 2 × 3 + 5 + 1

First, multiply 2 and 3

2a + b + 1 = 6 + 5 + 1

Add from left to proper beginning with 6 and 5

2a + b + 1 = 11 + 1

Lastly, add 11 and 1

2a + b + 1 = 12

Instance #2

Consider a + 4bab for a = 2 and b = -1

Substitute 2 for a and -1 for b

a + 4bab = 2 + 4(-1) – (2)(-1)

First, multiply 4 and -1 and in addition 2 and -1

a + 4b – ab = 2 + -4 – (-2)

Add the alternative when subtracting

a + 4b – ab = 2 + -4 + 2

Add from left to proper beginning with 2 and -4

a + 4b – ab = -2 + 2

Lastly, add -2 and a couple of

a + 4b – ab = 0 

Instance #3

Consider a + 4a ÷ b – 3b for a = 5 and b = -4

Substitute 5 for a and -4 for b

a + 4a ÷ b – 3b5 + 4(5) ÷ -4 – 3(-4)

First, multiply 4 and 5

a + 4a ÷ b – 3b = 5 + 20 ÷ -4 – 12

Divide 20 by -4

a + 4a ÷ b – 3b = 5 + -5 – 12

Add the alternative when subtracting

a + 4a ÷ b – 3b = 5 + -5 + -12

Add from left to proper beginning with 5 and -5

a + 4a ÷ b – 3b = 0 + -12

Add 0 and -12

a + 4a ÷ b – 3b = -12

A few examples displaying how one can consider algebraic expressions with exponents

Instance #4

Consider x3 + y2  for x = 2 and y = 2

x3 + y2 = (2)3 + (2)2

Consider the exponents

x3 + y2 = 8 + 4

Add 8 and 4

x3 + y2 = 12

Instance #5

Consider 3x2 – 4x + 2  for x = 4 

3x2 – 4x + 2 = 3(4)2 – 4(4) + 2

First, consider the exponent

3×2 – 4x + 2 = 3(16) – 4(4) + 2

Carry out the multiplications by multiplying 3 and 16 and in addition 4 and 4.

3×2 – 4x + 2 = 48 – 16 + 2

Add or subtract from left to proper beginning with 48 and 16

3×2 – 4x + 2 = 32 + 2

Add 32 and a couple of

3×2 – 4x + 2 = 34

Evaluating algebraic expressions with actual life examples

Instance #6

The algebraic expression 16t2 fashions the space in toes that an object falls throughout t seconds after being dropped from a sure distance. Discover the space an object falls after 10 seconds.

You simply want to guage 16t2 for t  = 10

16t2 = 16 × t × t

16t2 = 16 × 10 × 10

Multiply from left to proper beginning with 16 and 10

16t2 = 160 × 10

Multiply 160 and 10 

16t2 = 1600

The space the item fell is 1600 toes

Instance #7

Richard owns x vehicles and y vehicles. James owns 4 much less vehicles than Richard, however twice as many vehicles. Write an algebraic expression displaying the variety of autos James owns. If Richard owns 6 vehicles and a couple of vehicles, what number of car does James personal?

James owns 4 much less vehicles than Richard or x – 4

James owns twice as many vehicles as Richard or 2y

The variety of autos James owns is x – 4 + 2y

To learn the way many autos James owns, we have to consider the algebraic expression x – 4 + 2y for x = 6 and y = 2.

x – 4 + 2y = 6 – 4 + 2 × 2

First, multiply 2 and a couple of

x – 4 + 2y = 6 – 4 + 4

Add or subtract from left to proper beginning with 6 and 4

x – 4 + 2y = 2 + 4

At this level, you’ll be able to say that James owns 2 vehicles and 4 vehicles. However you might be on the lookout for the variety of autos he owns.

So, add 2 and 4

x – 4 + 2y = 6

The variety of autos James owns is 6 

Algebra ebook

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