Which graph shows the solution to the inequality x+3 2 – Which graph shows the solution to the inequality x+3 ≤ 2 embarks on an illuminating journey, unraveling the intricacies of this mathematical expression and guiding us toward a deeper understanding of its graphical representation.

Delving into the realm of inequalities, we embark on a quest to determine the values of x that satisfy the given inequality. By isolating the variable x and employing algebraic techniques, we uncover the solution and lay the groundwork for its graphical interpretation.

Solving the Inequality x+3 ≤ 2

In this article, we will solve the inequality x+3 ≤ 2 and graph its solution. An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥. Solving an inequality involves finding the range of values for the variable that make the inequality true.

Solving the Inequality

To solve the inequality x+3 ≤ 2, we need to isolate the variable x on one side of the inequality. We can do this by subtracting 3 from both sides of the inequality:

“`x+3

• 3 ≤ 2
• 3

x ≤

1

“`

Therefore, the solution to the inequality x+3 ≤ 2 is x ≤ -1.

Graphing the Solution, Which graph shows the solution to the inequality x+3 2

To graph the solution to the inequality x ≤ -1, we can use a number line. We mark -1 on the number line with a closed circle, since the inequality includes the equal sign. We then shade the region to the left of -1, since all values of x less than or equal to -1 satisfy the inequality.

“` <--|--o--------------------->

• ∞
• 1

“`

The graph of the solution to the inequality x ≤-1 is a closed circle at -1 and a shaded region extending to the left.

Interpreting the Graph

The graph of the solution to the inequality x ≤ -1 shows that all values of x less than or equal to -1 satisfy the inequality. For example, x = -2 and x = -1 both satisfy the inequality, while x = 0 and x = 1 do not satisfy the inequality.

FAQ Corner: Which Graph Shows The Solution To The Inequality X+3 2

What type of graph is used to represent the solution to x+3 ≤ 2?

A number line or an inequality graph can be used to represent the solution.

How do we determine the range of values for x that satisfy the inequality?

By isolating the variable x on one side of the inequality, we can determine the range of values that satisfy the inequality.

What is the significance of the solution to the inequality?

The solution to the inequality represents the range of values for x that make the inequality true.