Chapter 2: Q75. (page 88)

CHALLENGE Determine whether each sentence is sometimes, always, or never true. Explain your reasoning.
a. $x + x = x$
b. $x + 0 = x$

Short Answer

Expert verified

a.It is never true $2 x \neq x$ for any value of x except for 0.

b. It is always true for all values of x.

Step by step solution

Part a. Step 1. Concept of equation.

A mathematical statement with an 'equal to' symbol between two algebraic expressions (with any arithmetic operations) is known as an equation.

Part a. Step 2. Write the given information.

Given relation is $x + x = x$ .

Part a. Step 3. Calculation.

Consider the LHS of the given equation:

$\begin{array}{l} x + x \\ = 2 x \neq x \end{array}$

It is only true when $x = 0$ .

Hence, the given sentence is never true as $2 x \neq x$ for any value of x except for 0.

Part b. Step 1. Concept of the equation.

A mathematical statement with an 'equal to' symbol between two algebraic expressions (with any arithmetic operations) is known as an equation.

Part b. Step 2. Write the given information.

Given relation is $x + 0 = x$ .

Part b. Step 3. Calculation.

Consider the LHS of the given equation:

$\begin{array}{l} x + 0 \\ = x \end{array}$

Hence, the given sentence is always true for all values of x.

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CHALLENGE Determine whether each sentence is sometimes, always, or never true. Explain your reasoning.
a. $x + x = x$
b. $x + 0 = x$

Short Answer

Step by step solution

Part a. Step 1. Concept of equation.

Part a. Step 2. Write the given information.

Part a. Step 3. Calculation.

Part b. Step 1. Concept of the equation.

Part b. Step 2. Write the given information.

Part b. Step 3. Calculation.

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CHALLENGE Determine whether each sentence is sometimes, always, or never true. Explain your reasoning.a.x+x=xb.x+0=x

Short Answer

Step by step solution

Part a. Step 1. Concept of equation.

Part a. Step 2. Write the given information.

Part a. Step 3. Calculation.

Part b. Step 1. Concept of the equation.

Part b. Step 2. Write the given information.

Part b. Step 3. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Pure Maths

Probability and Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

CHALLENGE Determine whether each sentence is sometimes, always, or never true. Explain your reasoning.
a. $x + x = x$
b. $x + 0 = x$