Final answer:
To solve the inequality |5x+10|+1≤26, we consider two cases for the absolute value, resulting in the solution -7 ≤ x ≤ 3. This range is represented on a number line, with points -7 and 3 shaded to indicate all possible values of x that satisfy the inequality.
Step-by-step explanation:
The question asks us to solve the inequality |5x+10|+1≤26 and represent the solution on a number line. First, we handle the absolute value by considering two cases, one where the expression inside the absolute value is non-negative, and one where it is negative.
For the non-negative case:
- 5x + 10 + 1 ≤ 26
- 5x + 11 ≤ 26
- 5x ≤ 15
- x ≤ 3
For the negative case:
- -(5x + 10) + 1 ≤ 26
- -5x - 10 + 1 ≤ 26
- -5x - 9 ≤ 26
- -5x ≤ 35
- x ≥ -7
Combining the two cases, we get -7 ≤ x ≤ 3. We represent this on a number line by drawing a horizontal line and marking the points -7 and 3. The region between -7 and 3, including the endpoints, is shaded to represent all the possible solutions to the inequality.
To scale the x and y axes with the maximum x and y values, one would typically look at the function to find the maximums. However, since the function f(x) = 10, which is a constant function, the y value is always 10. Therefore, on a number line for f(x), only the x-axis is pertinent and can be scaled from -7 to 3 as discussed.