In order to identify equivalent linear expressions, we have to simplify the given function as much as possible and then we may check the simplified answer with the options given.

Let us see some example problems to understand the concept.

**Example 1 :**

Identify the equivalent expression of the following

−10b + b

Options :

(A) -9 + b (B) -9b (C) -9b²

**Solution :**

In the above expression both terms are having the same variable with same power. So both are like terms.

Since the signs of both terms are different, we have to subtract the smaller number from larger number and put greater number sign for the answer.

-10 b + b = -9b

Hence option B is correct.

**Example 2 :**

Identify the equivalent expression of the following

−x − 3x

Options :

(A) -4 + x (B) -4x² (C) -4x

**Solution :**

In the above expression both terms are having the same variable with same power. So both are like terms.

Since the signs of both terms are same, we have to add both numbers and put greater number sign for the answer.

−x − 3x = -4x

Hence option C is correct.

**Example 3 :**

Identify the equivalent expression of the following

−x − 3x

Options :

(A) -4 + x (B) -4x² (C) -4x

**Solution :**

In the above expression both terms are having the same variable with same power. So both are like terms.

Since the signs of both terms are same, we have to add both numbers and put greater number sign for the answer.

−x − 3x = -4x

Hence option C is correct.

**Example 4 :**

Identify the equivalent expression of the following

1 + 5v + v

Options :

(A) 1 + 6v (B) 1 + 6v² (C) 7v

**Solution :**

In the above expression 5v and v are like terms. So we an combine them.

1 + 5v + v = 1 + 6v

Since 1 and 65v are not like terms, we cannot combine them.

Hence the correct answer is option A.

**Example 5 :**

Identify the equivalent expression of the following

5k + 7k

Options :

(A) 12 k (B) 12k² (C) 5(k + 2)

**Solution :**

Since the signs of both terms are same, we have to add both numbers and put greater number sign for the answer.

5k + 7k = 12k

Hence option A is correct.

**Example 6 :**

Identify the equivalent expression of the following

a − 2 + 1 + 4a

Options :

(A) 5a - 3 (B) 3a (C) 5a - 1

**Solution :**

In the above expression "a" and "4a" are like terms, -2 and 1 are like terms.

= a − 2 + 1 + 4a

= a + 4a − 2 + 1

= 5a − 1

Hence option C is correct.

After having gone through the stuff given above, we hope that the students would have understood "Identify equivalent linear expressions".

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