Solution: Step 1: Reposition the inequality to place x on the left-hand side. x + 5 geq 8 Step 2: Isolate the variable x by eliminating constants from its side of the inequality. Step 2.1: Deduct 5 from both sides to maintain the balance of the inequality. x geq 8 - 5 Step 2.2: Compute the subtraction of 5 from 8. x geq 3 The solution is x geq 3. Step 3: Graph the solution on a number line, indicating that x is greater than or equal to 3. Knowledge Notes: - Inequalities are mathematical expressions involving the symbols , , 鈮? or 鈮? which indicate the relative size or order of two values. - When solving inequalities, it is important to perform the same operation on both sides of the inequality to maintain its balance. - When the variable is not on the preferred side (usually the left), it is common practice to rearrange the inequality to place the variable there. - Subtracting a number from both sides of an inequality does not change the direction of the inequality sign. - The solution to an inequality can be represented on a number line, where a filled-in circle indicates that the number is included in the solution (鈮?or 鈮?, and an open circle indicates that the number is not included ( or ). - The final solution set for the inequality should be expressed in a simplified form, with the variable isolated and all constants evaluated.

Graph 8< =x+5

The question involves graphing an inequality on a number line or coordinate plane. The inequality given is "8 ≤ x + 5". To graph this inequality, you would typically isolate the variable on one side to make it easier to understand where to place the points and how to shade the graph. The graph would show all the values of x that satisfy the given inequality (i.e., where x is greater than or equal to a certain value that you get once you solve the inequality for x).

$8 \leq x + 5$

Answer

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Solution:

Step 1:

Reposition the inequality to place $x$ on the left-hand side. $x + 5 \geq 8$

Step 2:

Isolate the variable $x$ by eliminating constants from its side of the inequality.

Step 2.1:

Deduct $5$ from both sides to maintain the balance of the inequality. $x \geq 8 - 5$

Step 2.2:

Compute the subtraction of $5$ from $8$. $x \geq 3$ The solution is $x \geq 3$.

Step 3:

Graph the solution on a number line, indicating that $x$ is greater than or equal to $3$.

Knowledge Notes:

Inequalities are mathematical expressions involving the symbols >, <, 鈮? or 鈮? which indicate the relative size or order of two values.
When solving inequalities, it is important to perform the same operation on both sides of the inequality to maintain its balance.
When the variable is not on the preferred side (usually the left), it is common practice to rearrange the inequality to place the variable there.
Subtracting a number from both sides of an inequality does not change the direction of the inequality sign.
The solution to an inequality can be represented on a number line, where a filled-in circle indicates that the number is included in the solution (鈮?or 鈮?, and an open circle indicates that the number is not included (> or <).
The final solution set for the inequality should be expressed in a simplified form, with the variable isolated and all constants evaluated.