Find the solution set to the inequality, express the solution in set notation. -6(x - 5) > 42 Show your work in vertical form
To solve the inequality -6(x - 5) > 42, let's first distribute the -6:
-6x + 30 > 42
Next, subtract 30 from both sides:
-6x > 12
Now, divide both sides by -6. Since we are dividing by a negative number, we need to reverse the inequality symbol:
x < -2
Therefore, the solution set in set notation is {x | x < -2}.
To solve the inequality -6(x - 5) > 42, let's start by simplifying the expression on the left side:
-6(x - 5) > 42
Distribute the -6:
-6x + 30 > 42
Subtract 30 from both sides to isolate the variable:
-6x > 42 - 30
-6x > 12
Now, divide both sides by -6. Remember that when we divide an inequality by a negative number, we need to reverse the inequality symbol:
x < 12 / -6
Simplifying the right side:
x < -2
Therefore, the solution set to the inequality -6(x - 5) > 42 is x < -2.
In set notation, we would express the solution as {-∞, -2}, which means all real numbers less than -2.
To find the solution set to the inequality -6(x - 5) > 42, let's start by simplifying the expression:
-6(x - 5) > 42
To simplify, we'll distribute -6 over the terms inside the parentheses:
-6x + 30 > 42
Now, let's isolate the variable by subtracting 30 from both sides of the inequality:
-6x > 42 - 30
Simplifying further:
-6x > 12
Next, we divide both sides of the inequality by -6. Since we are dividing by a negative number, we need to reverse the inequality sign:
x < 12/-6
Simplifying:
x < -2
Now that we have the solution, we can express it in set notation. In this case, the solution set consists of all values of x that are less than -2. So, the solution set in set notation is:
{x | x < -2}