Solution: Step 1: Increase both sides of the inequality by 4 to isolate x. The inequality becomes x geq 4. Step 2: Express the solution in various representations. In inequality notation, we have x geq 4. In interval notation, the solution is [4, infty). Knowledge Notes: To solve an inequality such as x - 4 geq 0, the goal is to isolate the variable on one side of the inequality sign. This is similar to solving an equation, but with an inequality, the solution is often a range of values rather than a single number. Here are the relevant knowledge points for this problem: 1. Inequality Manipulation: Just like with equations, you can add, subtract, multiply, or divide both sides of an inequality by the same non-zero number without changing the inequality's direction, as long as you multiply or divide by a positive number. If you multiply or divide by a negative number, you must reverse the direction of the inequality. 2. Isolating the Variable: To find the solution to an inequality, you want to get the variable by itself on one side. In this case, adding 4 to both sides removes the -4 from the left side and isolates x. 3. Inequality Notation: The solution to an inequality can be written in inequality form, such as x geq 4, which reads as "x is greater than or equal to 4." 4. Interval Notation: Interval notation is another way to express the set of solutions to an inequality. The interval [4, infty) includes all real numbers that are greater than or equal to 4. The square bracket, [, indicates that 4 is included in the set, while the parenthesis, ), indicates that the set does not include infinity (since infinity is not a number and cannot …

Solve for x x-4> =0

The given problem is a basic inequality question, where one is asked to find the value or range of values for the variable "x" that satisfy the inequality "x - 4 ≥ 0". The task involves determining when the expression "x - 4" is greater than or equal to zero, which will determine the solution set for "x".

$x - 4 \geq 0$

Answer

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Solution:

Step 1:

Increase both sides of the inequality by $4$ to isolate $x$ . The inequality becomes $x \geq 4$ .

Step 2:

Express the solution in various representations. In inequality notation, we have $x \geq 4$ . In interval notation, the solution is $[4, \infty)$ .

Knowledge Notes:

To solve an inequality such as $x - 4 \geq 0$ , the goal is to isolate the variable on one side of the inequality sign. This is similar to solving an equation, but with an inequality, the solution is often a range of values rather than a single number.

Here are the relevant knowledge points for this problem:

Inequality Manipulation: Just like with equations, you can add, subtract, multiply, or divide both sides of an inequality by the same non-zero number without changing the inequality's direction, as long as you multiply or divide by a positive number. If you multiply or divide by a negative number, you must reverse the direction of the inequality.
Isolating the Variable: To find the solution to an inequality, you want to get the variable by itself on one side. In this case, adding $4$ to both sides removes the $- 4$ from the left side and isolates $x$ .
Inequality Notation: The solution to an inequality can be written in inequality form, such as $x \geq 4$ , which reads as "x is greater than or equal to 4."
Interval Notation: Interval notation is another way to express the set of solutions to an inequality. The interval $[4, \infty)$ includes all real numbers that are greater than or equal to $4$ . The square bracket, $[$ , indicates that $4$ is included in the set, while the parenthesis, $)$ , indicates that the set does not include infinity (since infinity is not a number and cannot be reached).
Number Line Representation: Although not mentioned in the solution, another way to represent the solution to an inequality is on a number line, where you would shade all points to the right of $4$ and include a solid dot or circle at $4$ to indicate that it is part of the solution set.

Understanding these concepts is crucial for solving inequalities and representing their solutions correctly.