The line below is wrong. |3x| - x = 2x if x >=0, but is equal to -4x if x < 0.zeion said:Homework Statement
I need to find where these intersect:
y = |x|
3y - x = 8
Homework Equations
The Attempt at a Solution
I equate them:
|x| = (1/3)x + (8/3)
|x| - (1/3)x - (8/3) = 0
|3x| - x - 8 = 0
zeion said:|2x| - 8 = 0
|x| = 4
Is that right?
How do I get the other solution?
Factoring with absolute value is a mathematical process used to simplify expressions that contain absolute value symbols. Absolute value represents the distance of a number from zero on a number line and is always positive. Factoring with absolute value involves breaking down an expression into its factors, taking into account the absolute value of each factor.
Factoring with absolute value is typically used when simplifying algebraic expressions or solving equations. It can also be used to solve real-world problems involving distance or magnitude.
To factor an expression with absolute value, first identify the absolute value symbols and rewrite the expression as a positive or negative value. Then, factor the expression as you would normally do, taking into account the absolute value sign. Finally, simplify the expression by removing the absolute value signs and considering both positive and negative solutions.
Yes, you can factor out the absolute value symbol if it is the only factor in an expression. For example, in the expression |x+3|, the absolute value symbol can be factored out, resulting in |x+3| = 1. This can be rewritten as x+3 = 1 or x+3 = -1, giving two possible solutions.
Yes, there are a few rules to keep in mind when factoring with absolute value. One rule is that the absolute value of a product is equal to the product of the absolute values. Another rule is that the absolute value of a sum is less than or equal to the sum of the absolute values. These rules can be useful when simplifying expressions involving multiple absolute value symbols.