Chapter 1.3, Problem 39E

a.

To determine

To give an example of a linear equation that has no solution.

Answer to Problem 39E

  $3t+4=12+3t$

Explanation of Solution

Consider an equation:

  $3t+4=12+3t$

Calculation:

Now,

  $\Rightarrow 3t+4=12+3t$

  $\Rightarrow 3t+4-3t=12+3t-3t$ (Subtracting 3t on both sides)

  $\Rightarrow 4=12$

The above equality is mathematically incorrect which means there is no possible solution for the given expression.

Conclusion:

Hence, it is justified that the given equation is correct to the context with no solution.

b.

To determine

To give an example of a linear equation that has infinitely many solutions

Answer to Problem 39E

  $3(4g+6)=2(6g+9)$

Explanation of Solution

Consider an equation:

  $3(4g+6)=2(6g+9)$

Calculation:

Now,

  $\Rightarrow 3(4g+6)=2(6g+9)$

  $\Rightarrow 12g+18=12g+18$

  $\Rightarrow 12g+18-12g=12g+18-12g$ (Subtracting 12g on both sides)

  $\Rightarrow 18=18$

The above equality is always true no matter what the value of g comes out to be.

Hence, the expression is an identity, which means any value of g will satisfy the given expression.

Conclusion:

Hence, it is justified that the given equation is correct to the context with infinitely many solution.