James determined that these two expressions were equivalent expressions using the values of x=4 and

4(2)+1 = 9
You plug in 2 in place of x and multiply and that is your answer

1 - Correct

2 - incorrect

3- incorrect

4 - incorrect

5 - Correct

Step-by-step explanation:

Notice that

3x  + 5 + 4x -1  =    3x + 4x + 5 -1 = 7x  + 4

therefore the two expressions are equivalent for ANY number, specially x = 4 and x = 6 therefore

1 - Correct

Since that is true for all numbers  

2 - incorrect

3- incorrect

4 - incorrect

The expressions are equivalent for all numbers therefore

5 - Correct

9

Step-by-step explanation:

So when solving algebraic equations, it is always important to keep in order of operations.

1.Parenthesis

2.Exponents

3.Multiplication

4.Division

5.Addition

6.Subtraction

In this case, it is multiplication  first, (4x)

and lastly addition (4x+1)

In this case we do not know what x is so 4x cannot be simplified any further.

Now replace x with 2 and plug it in

4*2=8

8+1=9

AnsSolution:The Expression P = 7 x + 4Q = 3 x + 5 + 4 x -1Adding like terms , i.e term containing variables and term containing constantsQ = 3 x + 4 x + 5 -1 [You must be thinking why i have written this, keep in mind Commutative law of addition which is , a + b = b  + a, i.e in this expression , 5 + 4 x = 4 x + 5]So, Q = 7 x + 4As you can see both P and Q are identical Expressions.Now we will check each and every option.1. When x= 2, P =Q= 7 × 2 + 4= 14 + 4= 18→→→→(True)2. As for x=4,6 P = Q = 7 × 4 +4=28 + 4=32P = Q= 7× 6 +4 = 42 +4=46As , explained above, We saw that both the expressions P and Q are identical.So , There are infinite values of x , for which these Expression P and Q are identical.Statement 2 is not true i.e False.3. Statement 3 , is false.→→→[Explained above]4. True →→The expressions have equivalent values for any value of x.5. False →→→The expressions should have been evaluated with one odd value and one even value.6. False →→→As ,P =Q Both expressions are identical. [When x=0, the first expression has a value of 4 and the second expression has a value of 5.]7. True, As, P = Q, so both the expression P and Q have same value for x=8.

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Step-by-step explanation:

Answer with explanation:

Two or more Algebraic expressions are said to be equivalent, if both the expression produces same numerical value , when variable in the expressions are replaced by any Real number.

The two expressions are

1. 7 x +4

2. 3 x +5 +4 x =1

Adding and subtracting Variables and constants

→7 x +5=1

→7 x +5-1

→7 x +4

→ When x=2,

7 x + 4 =7×2+4

=14 +4

=18

So, Both the expression has same value =18.

→So, by the definition of equivalent expression, when ,you substitute , x by any real number the two expression are equivalent.

Correct options among the given statement about the expressions are:

1.When x = 2, both expressions have a value of 18.

2.The expressions have equivalent values for any value of x.

3.The expressions have equivalent values if x = 8.

Solution:

The Expression

P = 7 x + 4

Q = 3 x + 5 + 4 x -1

Adding like terms , i.e term containing variables and term containing constants

Q = 3 x + 4 x + 5 -1 [You must be thinking why i have written this, keep in mind Commutative law of addition which is , a + b = b  + a, i.e in this expression , 5 + 4 x = 4 x + 5]

So, Q = 7 x + 4

As you can see both P and Q are identical Expressions.

Now we will check each and every option.

1. When x= 2,

P =Q= 7 × 2 + 4= 14 + 4= 18→→→→(True)

2. As for x=4,6

P = Q = 7 × 4 +4=28 + 4=32

P = Q= 7× 6 +4 = 42 +4=46

As , explained above, We saw that both the expressions P and Q are identical.

So , There are infinite values of x , for which these Expression P and Q are identical.

Statement 2 is not true i.e False.

3. Statement 3 , is false.→→→[Explained above]

4. True →→The expressions have equivalent values for any value of x.

5. False →→→The expressions should have been evaluated with one odd value and one even value.

6. False →→→As ,P =Q Both expressions are identical. [When x=0, the first expression has a value of 4 and the second expression has a value of 5.]

7. True, As, P = Q, so both the expression P and Q have same value for x=8.

The expressions 7x + 4 and 3x + 5 + 4x = 1 are equivalent for every value of x.

Step-by-step explanation:

Expressions - 7x + 4 and 3x + 5 + 4x = 1.

1. When x = 2, both expressions have a value of 18. Let's find out:

1st expression : 7(2) + 4 = 14+4 = 18

2nd expression : 3(2) + 5 + 4(2) = 1

or 6 + 5 + 8 - 1 = 18

Values of both the expressions is 18, hence it is correct statement.

2.The expressions are only equivalent for x = 4 and x = 6.

This is incorrect statement as we just calculated above that the expressions are equivalent for x = 2. Hence, it is incorrect.

3. The expressions have equivalent values for any value of x.

Say, x = 0, then,

7x + 4 = 7 (0) + 4 = 4 and,

3x + 5 + 4x - 1 =  3(0) + 5 + 4(0) - 1  = 5-1 = 4

The statement holds.

Let's try again for x = 12,

7x + 4 = 7(12) + 4 = 88 and,

3x + 5 + 4x - 1 =  3(12) + 5 + 4(12) - 1  = 36 + 5 + 48 -1 =  88

Let's try again for x = 13,

7x + 4 = 7(13) + 4 = 95 and,

3x + 5 + 4x - 1 =  3(13) + 5 + 4(13) - 1  = 39 + 5 + 52 -1 =  95

Clearly, it holds for every value of x, whether it is odd or even. Hence, it is correct statement.

Trick: 7x + 4 = 0(1) and,

3x + 5 + 4x = 1

Rearranging the terms of above expression, we get,

(3x + 4x) + (5 - 1) =0

or 7x + 4 = 0...(2)

clearly both (1) & (2) are equivalent.

When x = 2, both expressions have a value of 18

The expressions have equivalent values for any value of x.

The expressions have equivalent values if x = 8.​

Step-by-step explanation:

7x+4 and 3x+5+4x-1

7(2)+4 = 18 and 3(2)+5+4(2)-1 = 18

7x+4 and 3x+5+4x-1

7x + 4 and 7x + 4

Idnetical, equal for all x

When x = 2, both expressions have a value of 18

The expressions have equivalent values for any value of x.

The expressions have equivalent values if x = 8.​

Step-by-step explanation:

7x+4            3x+5+4x-1

Let x=2

7*2 +4 = 18

3*2+5+4*2-1 = 6+5+8-1=18

When x = 2, both expressions have a value of 18

The expressions are only equivalent for x = 4 and x = 6.

False, they are both equal when x=2

Try x=1

7+4 =11    3+5+4-1 = 11

They are equal with an odd value

When x = 0, the first expression has a value of 4 and the second expression has a value of 5.

4   5-1 =4   false

The expressions are only equivalent when evaluated with even values.  false

The expressions should have been evaluated with one odd value and one even value.  my best guess is false, if it is true for 2 values it is true for all values

The expressions have equivalent values if x = 8.​  true

7*8 +4 = 60    3(8)+5 +4(8) -1 =60

The expressions have equivalent values for any value of x.

7x+4     3x+4x +5-1  = 7x+4

They are always equal

Y = -(-2)^2 + 4(-2) + 1
y = -4 - 8 + 1
y = -11