No, they're not. For example, if you multiply both sides of an equation by, say, -1, you get a new equation that is equivalent to the one you started with.Scheuerf said:How would I solve the inequality (X-4)/X>0. I thought that inequalities were solved in the same way equations were
Scheuerf said:, but when I solve that way I get X>4 which isn't the entire answer.
Or, more simply, just multiply both sides of the inequality by x2, first making a note that x cannot be zero. For x ≠ 0, x2 > 0, so the direction of the inequality doesn't change.Svein said:Well, what you do is:
x-4: Negative when x<4, positive when x>4
x: Negative when x<0, positive when x>0
Expression: Positive when x<0 (neg. and neg. makes pos.), negative when 0<x<4 and positive when x>4
A simple inequality is a mathematical statement that compares two quantities using symbols such as <, >, ≤, or ≥. It states that one quantity is greater than or less than another quantity.
To graph a simple inequality, first rewrite it in slope-intercept form (y = mx + b). Then, plot the y-intercept (b) on the y-axis and use the slope (m) to find a second point on the line. Finally, shade the area above or below the line depending on the inequality symbol.
The solution set of a simple inequality is the set of all values that make the inequality true. It can be represented by a graph or written in interval notation.
Solving a simple inequality is similar to solving an equation, but there are a few key differences. When solving an inequality, the solution may be a range of values rather than a single value. Also, when multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality symbol must be reversed.
A strict inequality uses the symbols < and > and indicates that the two quantities are not equal to each other. A non-strict inequality uses the symbols ≤ and ≥ and indicates that the two quantities can be equal to each other.