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
To solve the inequality 26 + 6b > 2(3b + 4), follow these steps:
Step 1: Distribute the 2 to the terms inside the parentheses:
26 + 6b > 6b + 8
Step 2: Simplify the equation by combining like terms:
6b - 6b > 8 - 26
0 > -18
Step 3: Since 0 is always greater than any negative number, the inequality 0 > -18 is true for all real numbers.
Step 4: However, since there are no restrictions given in the original inequality, we need to determine if any limitations exist.
Comparing the inequality with the solution sets b < 1 1/2 and b > 1 1/2, we find that none of these solutions satisfy the original inequality.
Step 5: Therefore, the solution to the inequality 26 + 6b > 2(3b + 4) is NO SOLUTION, as there are no values of b that make the inequality true.
To solve the given inequality, we will start by simplifying the expression on the right-hand side:
26 + 6b > 2(3b + 4)
First, distribute the 2 to the terms inside the parentheses:
26 + 6b > 6b + 8
Next, let's simplify the inequality:
Subtract 6b from both sides to isolate the constant term:
26 > 8
Since this statement is true (26 is indeed greater than 8), the inequality holds for all real numbers. Therefore, there is no restriction on the value of b, and the solution set is all real numbers.
To summarize:
Solution set: All real numbers (no restriction on b).
Note: There is no need to graph the solution set in this case since it encompasses all real numbers.