Homework 15 (due 3/25)

Recall: to solve an equation means to find all solutions, i.e. all numbers x that make the equality true.

Solve the following equations over the set of real numbers (i.e. find all real solutions of these equations). Show all steps of your solutions. Make sure that you can justify each step (recall that you can add the same number to both sides of an equation, subtract the same number from both sides of an equation, multiply both sides of an equation by the same number, or divide both sides of an equation by the same nonzero number. Be careful with division: if dividing by a variable/expression, remember that division is legal only when the variable/expression is nonzero!)

• 2x+5=19
• 2x+5=4x+11
• 3x=5x
• 3x+(x/2)=5-(x/3)
• 3/x=9
• x²=16
• x³=-27
• (x-3)(x+5)=0