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How does solving linear inequalities differ from solving linear equations?
Linear inequalities are equations, but instead of an equal sign, it has either a greater than, greater than or equal to, less than, or a less than or equal to sign. Both can be graphed. Solving linear equations mainly differs from solving linear inequalities in the form of the solution. 1. Linear equation. For each linear equation in x, there is only one value of x (solution) that makes the equation true. Example 1. The equation: x - 3 = 7 has one solution, that is x = 10. Example 2. The equation: 3x + 4 = 13 has one solution that is x = 3. 2. Linear inequality. On the contrary, a linear inequality has an infinity of solutions, meaning there is an infinity of values of x that make the inequality true. All these x values constitute the "solution set" of the inequality. The answers of a linear inequality are expressed in the form of intervals. Example 3. The linear inequality x + 5 < 9 has as solution: x < 4. The solution set of this inequality is the interval (-infinity, 4) Example 4. The inequality 4x - 3 > 5 has as solution x > 2. The solution set is the interval (2, +infinity). The intervals can be open, closed, and half closed. Example: The open interval (1, 4) ; the 2 endpoints 1 and 4 are not included in the solution set. Example: The closed interval [-2, 5] ; the 2 end points -2 and 5 are included. Example : The half-closed interval [3, +infinity) ; the end point 3 is included.
Where is the stern octagon on page 8 9 i you spy extreme challenger?
Hint 1 : It's on page 8. Hint 2 : The octagon is red. Hint 3 : It comes in the form of a roadsign.
What is the difference between 7 less than a number and 7 is less than a number?
7 less than a number is an algebraic expression. Given the number the expression can be evaluated. 7 is less than a number is a statement in the form of an inequality. It is true for some values of the number and not for others.
How do you write out Six times a number minus five is less than twice the number plus ten?
To write out the given statement algebraically, you would start by defining the variable for the number, let's say it is represented by 'x'. The equation would be: 6x - 5 < 2x + 10. This equation represents the statement "Six times a number minus five is less than twice the number plus ten" in algebraic form. To solve this inequality, you would isolate the variable 'x' by performing operations to simplify and find the range of values that satisfy the inequality.
What triangle measures 2m 4m and 7m?
The triangle with side lengths of 2m, 4m, and 7m does not form a valid triangle. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side according to the Triangle Inequality Theorem. In this case, 2m + 4m is less than 7m, violating the theorem. Therefore, a triangle with these side lengths cannot exist in Euclidean geometry.
