Explain the difference between simplifying an expression and solving an equation. Give an example of each.?

Suppose we want to find the zeros of x^2 - x

This can be simplified by factoring out the x

x(x - 1) = 0

However we still haven't solved the equation. But while we didn't solve it, simplifying made it much easier to solve.

Simplifying an expression means rewriting it without determining a value for the variables. For example

3x + 4x + 6 + 5

can be simplified to

7x + 11

simplifying does not need a comparison operator such as an equals sign.

However, solving an equation requires a comparison operator. For example

3x + 4x + 6 + 5 = 2

7x + 11 = 2

Subtract 11

7x = 2 - 11 = -9

Divide by 7

7x/7 = x = -9/7

When you are asked to simplify an expression, all you need to do is re-arrange the equation you are given thru knowing specific rules to have variables cancel out and to be left with a simpler equation...

X^3 - 5x + 14x^2 - 3x^3 + 5x^2 - 7 + 17x - 1

to simplify this , you would collect like terms and perform the simple math...

x^3 - 3^3 + 14x^2 + 5x^2 - 5x + 17x - 7 - 1

= - 2x^3 + 19x^2 + 12x -8

Simplifying an equation is when you actually solve for "x" or any other variable that you may be working with.... here is a simple example....

x = log base5 ( 125^2)

to simplify this you would need to kno the log rules..

log base5 (125^2) = log base5 (5^3)^2

= log base5 ( 5^6) = 6 * log base5 (5 ) = 6

therefore you SOLVED for x = 6

Solving an equation has an equal sign 10x-5=50 and simplifying an expression doesn't have an equal sign (24x+4)(10X+5).

ok answering a question, you would give a value for x

ex: 12x=144 x=12 in this situation

simplifying meens that you put it together

ex: 3x+9x=144 in this case you add the x's and again get x to = 12

also, you cant always solve for x when you simplify, you may not get an answer at all.

ex: 3x+9=5x(5)+4-y