Solve the following equations by hand using Maple's equation handling functions. Show your work by using lhs(%) and rhs(%).

2x + 4 = 28

> 2*x+4=28;

> lhs(%)-4=rhs(%)-4;

> lhs(%)/2=rhs(%)/2;

4x+24=60

> 4*x+24=60;

> lhs(%)-24=rhs(%)-24;

> lhs(%)/4=rhs(%)/4;

> (4*x*(sin(x)^2+cos(x)^2)+1)/4=5*(-tan(x)^2+sec(x)^2);

> simplify(%);

> lhs(%)*4=rhs(%)*4;

> lhs(%)-1=rhs(%)-1;

> lhs(%)/4=rhs(%)/4;

Bonus:

2^2x+4 = 2^3x-1

> 2^(2*x+4)=2^(3*x-1);

> log[2](lhs(%))=log[2](rhs(%));

> simplify(%); #Instead of removing the logarithms as expected, Maple used the laws of logs to simplify them.

> lhs(%)*ln(2)=rhs(%)*ln(2);

> simplify(%);

> lhs(%)/ln(2)=rhs(%)/ln(2);

> simplify(%);

> lhs(%)-2*x+1=rhs(%)-2*x+1; #You can combine operations into one statement.

> rhs(%)=lhs(%);

As you can see from doing this problem, this method of solving equations isn't the best in all cases.

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