Final answer:
To solve the system of inequalities 3x≤23 OR 4x+26≥6, we solve each inequality separately, giving x≥7.67 and x≥-5, respectively. The solution is the union of both, meaning x can be any number within the range of those two solutions.
Step-by-step explanation:
When solving the system of inequalities 3x≤23 OR 4x+26≥6, we need to find the set of all possible values of x that satisfy at least one of these inequalities. To do so, let's solve each inequality separately.
For the inequality 3x≤23:
1. Divide both sides by 3 to isolate x: x ≤ 23 / 3
2. Calculate the result: x ≤ 7.67
Now, for the inequality 4x+26≥6:
1. Subtract 26 from both sides of the inequality: 4x ≥ 6 - 26
2. Simplify the right side: 4x ≥ -20
3. Divide both sides by 4 to isolate x: x ≥ -5
The solution to the system is the union of the two solutions since 'OR' connects the inequalities. This results in:
x ≥ -5 OR x ≤ 7.67
This means x can be any number greater than or equal to -5 as well as any number less than or equal to 7.67. Therefore, any such values for x would make at least one of the inequalities true.