Chapter 2: Q.31. (page 111)

Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.
$23 z + 19 = 3 (5 z - 9) + 8 z + 46$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

The given equation is $23 z + 19 = 3 (5 z - 9) + 8 z + 46$ .

Step 2. Apply the distributive property.

Simplify the equation.

$23 z + 19 = 3 (5 z - 9) + 8 z + 46 23 z + 19 = 3 \times 5 z - 3 \times 9 + 8 z + 46 23 z + 19 = 15 z - 27 + 8 z + 46 23 z + 19 = 23 z + 19$

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

Subtract $23 z$ from each side.

$23 z + 19 - 23 z = 23 z + 19 - 23 z 19 = 19$

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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Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.
$23 z + 19 = 3 (5 z - 9) + 8 z + 46$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Apply the distributive property.

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

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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

Step by step solution

Step 1. Given information.

Step 2. Apply the distributive property.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Calculus

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Study anywhere. Anytime. Across all devices.

Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.
$23 z + 19 = 3 (5 z - 9) + 8 z + 46$