The inequality 2x ≤ 10 can be solved step by step to understand what values of x satisfy the inequality.
Step 1: Solving the Inequality
- To isolate x, divide both sides of the inequality by 2:
- x ≤ 5
This inequality means that x can take on any value that is less than or equal to 5.
Step 2: Graphing the Solutions
- On a number line, draw a solid dot at 5 to indicate that 5 is included in the solution set (because of the ‘less than or equal to’ part).
- Then, shade the line to the left of 5 to represent all of the numbers less than 5. This shading shows that every number to the left on the number line is a valid solution.
Step 3: Visual Representation
Here’s how you might visualize the graph:
- —–|—–|—–|—–|—–|—–|—–|—–|
- …3…4…5…6…
-  less than or equal to … ●
This representation clarifies that any x-value to the left of and including 5 will satisfy the original inequality.
In conclusion, the graph representing the solutions to the inequality 2x ≤ 10 is a number line with a solid dot at 5 and shading extending to the left.