Solve and graph −6x+7≤−29−6𝑥+7≤−29.

The given inequality is −6x + 7 ≤ −29.

Step 1: Subtract 7 from both sides of the inequality to isolate the term with x on one side. This gives us:

−6x ≤ −29 - 7 −6x ≤ −36

Step 2: Divide both sides of the inequality by -6 to solve for x. Remember that when you divide or multiply an inequality by a negative number, the direction of the inequality sign changes. So, we get:

x ≥ 6

So, the solution to the inequality is x ≥ 6.

To graph this solution on a number line:

1. Draw a number line and mark the point that corresponds to 6.
2. Since x is greater than or equal to 6, shade the portion of the number line that is to the right of 6.
3. Since 6 is included in the solution (because of the "or equal to" part of "greater than or equal to"), draw a closed circle at 6 to indicate this.

And that's your solution and its graph