Solve the inequality. Write the solution in set-builder notation. - 2(9x + 6) > - 12 - 18x Solve the inequality. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (Type an inequality.) OB. The solution is all real numbers. O c. There is no solution.
-2(9x + 6) > -12 - 18x
-18x - 12 > -12 - 18x
Since the x terms cancel out, we are left with -12 > -12, which is not true.
Therefore, there is no solution.
The answer is (c) There is no solution.
To solve the inequality -2(9x + 6) > -12 - 18x, you can start by distributing -2 to the terms inside the parentheses:
-18x - 12 > -12 - 18x
Next, we can simplify by canceling out the -18x terms on both sides:
-12 > -12
Since -12 is not greater than -12, the inequality is not true. Therefore, the solution is no solution (c. There is no solution).
To solve the inequality -2(9x + 6) > -12 - 18x, we can first simplify both sides of the inequality:
-18x - 12 > -12 - 18x.
Next, we can subtract -18x from both sides to eliminate the x terms on the right side:
-12 > -12.
Now, we can see that both sides of the inequality are equal, -12 > -12. This means that the inequality is true for all real values of x. Therefore, the solution to the inequality is all real numbers.
The correct choice is B. The solution is all real numbers.