Question

Make a graph that shows the solution to x+3≤7

Answer 1

Here is the solution graph for the inequality x + 3 ≤ 7:

First, we draw a number line.

-∞ -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 +∞

The inequality x + 3 ≤ 7 represents all the values of x that are less than or equal to 7 when 3 is added to them.

To graph this, we start at 7 on the number line, as this is the equal sign in the inequality. Then, we move 3 units to the left since x is being added by 3.

So, starting from 7, we move 3 units to the left and mark a closed circle at 4. The circle indicates that 4 is included in the solution set since it satisfies the inequality.

Now, we draw a line to the left from the closed circle towards -∞. This indicates all the values of x less than or equal to 7 when 3 is added to them.

The final graph would look like this:

-∞.....[=======●-------------]
-6 -4 7 +∞

This graph visually shows all the values of x that satisfy the inequality x + 3 ≤ 7.