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Chapter 2: Q.31. (page 111)

Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.

23z+19=35z-9+8z+46

Short Answer

Expert verified

The equation is an identity and the solution of this equation is "all real numbers".

Step by step solution

01

Step 1. Given information.

The given equation is23z+19=35z-9+8z+46.

02

Step 2. Apply the distributive property.

Simplify the equation.

23z+19=35z-9+8z+4623z+19=3脳5z-3脳9+8z+4623z+19=15z-27+8z+4623z+19=23z+19

03

Step 3. Collect all variables terms on one side of the equation.

Subtract 23zfrom each side.

23z+19-23z=23z+19-23z19=19

This is a true statement.

It means the equation is true for any value of the variable.

So, the equation is an identity.

Hence, the solution of this equation is "all real numbers".

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