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when the variable is to the power one you will only have one answer....
2 solutions when to the power 2
3 when cubed etc.
note: when multiple answers it is possible for answers to repeat ex. x^2+4x+4 =0
would factor to (x+2)(x+2)=0 so x=-2 and x=-2 there is only one answer but it repeats. [Note: the graph of this parabola will 'just touch' the x-axis at x = -2]
Also, it may seem that there is only one solution, for example x³ - 5x² + 8x - 6 = 0 looks like it only has one solution at x = 3 (as the graph of it will only cross the x-axis once at x = 3), but there are two more solutions which require the use of complex numbers, in this case namely x = 1 + i, and x = 1 - i (where i = √-1).
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Why do you isolate the variable on one side the the equation when solving a linear equation?
Isolating a single variable in terms of the rest of the equation provides a solution to that variable. That is, if you know the equation that equals the variable, then you can figure out its value.
What is the number that can replace a variable in an equation to make it a true equation?
The number that can replace a variable in an equation to make it a true equation is called the solution or root of the equation. This number satisfies the equation when substituted for the variable. In algebra, finding the solution involves solving for the variable by performing various operations to isolate it on one side of the equation. The solution is the value that balances both sides of the equation, making it true.
What is A number that makes a equation true?
The solution set is the answers that make an equation true. So I would call it the solution.
Why do we represent the solution to an inequality with a graph on a number line but we don't do the same for the solution to an equation?
An equation has an equal sign, which means that we know what the variable is equal to :)
If the discriminant of a quadratic equation equals zero what is true of the equation?
It has one real solution.
