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What is3 x-4 is an expression or equation?
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What is the solution set for the equation 2x plus 4?
2x + 4 is an expression, not an equation. There can be no solution set for an expression.
What is the equation 2 to the power of 4?
2 to the power of 4 is an expression, it is not an equation.
Do all algebraic expressions have to have variables for example would 3 plus 4 equals 9 be an expression or would it need to be n plus 4 equals 9 to be an expression?
3 + 4 = 9 is not an expression, it is an equation (which happens to be false). An equation without a variable is simply a statement which is either true (a tautology) or false. It's main use is probably at the end of a proof where you may show that the left hand side of some equation is numerically the same as the right hand side which proves your proposition. n + 4 = 9 is also not an expression, but an equation. An equation with a variable can divide the domain into distinct partitions such that the equation is true if the value of the variable is within those partitions and not if they are outside. This may enable you to derive further information about he variable(s).
How do you write an algebraic expression for the sum of a number and -6 is 4?
You cannot write an algebraic expression for that, you need an equation. The equation is n - 6 = 4
