Solve the inequality graph the solution set 26+6b>2(3b+4) answers are all real numbers, b<1 1/2, b>1 1/2,, no solution
no solution is correct.
actually, I change my answer. it is true for all b.
To solve the inequality 26 + 6b > 2(3b + 4), we will follow these steps:
Step 1: Distribute the 2 on the right side of the inequality:
26 + 6b > 6b + 8
Step 2: Simplify the equation by subtracting 6b from both sides:
26 > 8
Step 3: Since 26 is greater than 8, this inequality is always true. This means the solution set includes all real numbers.
Now, let's graph the solution set on the number line:
Since the solution set includes all real numbers, we draw a number line with no breaks or restrictions.
To indicate that the inequality includes all real numbers, we use the symbol "(-∞, +∞)" or shade the entire number line.
However, there is an additional condition mentioned in the question, which restricts the value of b. According to the question, b must be less than 1 1/2 (or b < 1.5) or greater than 1 1/2 (or b > 1.5).
Thus, we need to shade the number line based on the condition:
- Shade to the left of 1 1/2 to represent b < 1 1/2
- Shade to the right of 1 1/2 to represent b > 1 1/2
Therefore, the graph of the solution set will be a number line with a shaded area to the left of 1 1/2 and to the right of 1 1/2, with the portion in between left unshaded.
Finally, we observe that the given inequality has no solution since it is always true for all real numbers, but we do not have a specific value for b.
So, the answer to the inequality 26 + 6b > 2(3b + 4) is: b < 1 1/2, b > 1 1/2, and no solution.