5x−6≤−1+1+5x−6 The solution to the inequality is x≤0.
Since x can take any value less than or equal to 0, we represent this on the number line as a closed circle at 0 (indicating equality) and an arrow pointing to the left, indicating all values less than 0.
The given inequality is solved by simplifying the expression on both sides of the inequality sign. Combining like terms and performing basic arithmetic operations, we find that x≤0 is the solution. This means that any value of x less than or equal to 0 satisfies the inequality.
The graph visually represents this solution on a number line. The closed circle at 0 indicates that 0 is included in the solution (because of the ≤ sign). The arrow extending to the left from the circle signifies that all values less than 0 are also solutions to the inequality.
Inequalities and their solutions are crucial in mathematics and real-world applications. They help describe relationships between variables and establish conditions for various scenarios. Graphically representing solutions on a number line enhances our understanding of the solution set and facilitates communication of mathematical concepts. In this case, the solution x≤0 indicates a range of values for x that make the original inequality true.