James determined that these two expressions were equivalent expressions using the values of x=4 and x =6 which statements are true? check all that apply. 7x+4 and 3x+5+4x-1 when x=2, both expressions have a value of 18. the expressions are only equivalent for x=4 and x=6 the expressions are only equivalent when evaluated with even values. the expressions have equivalent values for any value of x. the expressions should have been evaluated with one odd value and one even value. when x=0, the first expression has a value of 4 and the second expression has a value of 5. 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.

here is a big fat