(red added by me)science_rules said:(x - 2)^3 = x^2(x - 6)
= (x^3 - 8) = (x^3 - 6x^2)
(x^3 - 8) = (x^3 - 6x^2)
-x^3 -x^3
= -8 = -6x^2
I am not sure how to solve this for x
You can start by removing the terms that appear on both sides of the equation. Then see what remains.science_rules said:I know I am supposed to even out the inequality by subtracting and adding to each side but I am still not sure how to solve for x
Correct. You can simplify this to 8/12 or 2/3.science_rules said:I meant: x = -8/-12
Don't connect pairs of equations with '='. An equation is not "equal to" another equation. One equation can be equivalent to another equation (same solution set for both) or one equation can imply another equation. There are separate symbols for each of these relationships, but in your case it would be OK to not use any symbol at all between the successive equations.science_rules said:(x - 2)^3 = x^2(x - 6)
= (x-2)(x-2)(x-2) = x^3 - 6x^2
= (x^2 - 2x -2x + 4) (x-2)
= (x^2 - 4x + 4)(x-2)
= x^3 - 6x^2 + 12x -8
x^3 - 6x^2 + 12x -8 = x^3 -6x^2 ?
You should never leave an answer like this. -8/-12 is the same as 8/12, which can be simplified to 2/3.science_rules said:I meant: x = -8/-12
To solve a linear equation, you need to isolate the variable on one side of the equation. This is done by performing the same operation on both sides of the equation until the variable is alone on one side. Then, you can determine the value of the variable by solving the equation using basic algebraic principles.
A linear equation is an algebraic equation in which the highest power of the variable is one. It can be written in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. Linear equations are used to represent relationships between two variables that can be graphed as a straight line.
The steps to solve a linear equation include: 1) Simplify both sides of the equation by combining like terms, 2) Isolate the variable term by performing inverse operations on both sides, 3) Simplify the equation to get the value of the variable, and 4) Check your answer by plugging it back into the original equation.
Yes, you can solve a linear equation with fractions or decimals. The key is to first eliminate any fractions by multiplying both sides of the equation by the least common denominator (LCD). For decimals, you can convert them into fractions by moving the decimal point to the right until you have a whole number, and then simplify the resulting fraction.
Yes, a linear equation can have one, infinite, or no solution. When solving a linear equation, you may encounter equations where the variable is eliminated and the statement becomes either true or false. In this case, the equation has no solution. If the variable is eliminated and the statement becomes always true, then the equation has infinite solutions. Otherwise, there will be one unique solution for the variable.