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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 true2x鈮�x for any value of x except for 0.

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

Step by step solution

01

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.

02

Part a. Step 2. Write the given information.

Given relation is x+x=x.

03

Part a. Step 3. Calculation.

Consider the LHS of the given equation:

x+x=2x鈮�x

It is only true when x=0.

Hence, the given sentence is never true as2x鈮�x for any value of x except for 0.

04

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.

05

Part b. Step 2. Write the given information.

Given relation is x+0=x.

06

Part b. Step 3. Calculation.

Consider the LHS of the given equation:

x+0=x

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

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