Explain why there are either two, one, or no solutions for absolute value equatins. Demonstrate an example for each
2 answers:
Absolute value equations |a|=b have two solutions only if b>0, because it means that a=b or a=-b. Example:
Absolute value equations |a|=b have one solution only if b=0, because 0=-0. Example:
Absolute value equations |a|=b have no solution only if b<0, because absolute value can't have a negative value. Example:
Absolute value equations |a|=b have one solution only if b=0, because 0=-0. Example:
Absolute value equations |a|=b have no solution only if b<0, because absolute value can't have a negative value. Example:
You might be interested in
We use algebraic equations in our daily lives without knowing it. For example, when we go shopping, calculate grocery expenses, or even fill our gas tanks, we are using equations. Let's say we needed to fill our gas tank, but we only had $15.00 to do so. If the price of gas is $3.00 per gallon, how many gallons could we buy? We use the simply algebraic equation of 
to calculate the total gallons that can be bought. x = the money we have. y = price per gallon of gas. 
= 5. So with $15.00, we can buy 5 gallons of gas; and that is just one example of using an algebraic equation in everyday life!