Solve the inequality. Write the solution in set-builder notation.
- 4x - 18 => - 34
To solve the inequality -4x - 18 ≥ -34, we need to isolate the variable x.
First, we can add 18 to both sides:
-4x - 18 + 18 ≥ -34 + 18
-4x ≥ -16
Then, divide both sides by -4, remembering to flip the inequality sign since we are dividing by a negative number:
-4x/(-4) ≤ -16/(-4)
x ≤ 4
The solution to the inequality is x ≤ 4.
In set-builder notation, this can be written as:
{x | x ≤ 4}
To solve the inequality -4x - 18 ≥ -34, we will go through the following steps:
Step 1: Start by moving the constant term to the opposite side of the inequality sign.
-4x ≥ -34 + 18
Simplifying the right side we get:
-4x ≥ -16
Step 2: Divide both sides of the inequality by the coefficient of x, which is -4. Remember that when dividing an inequality by a negative constant, we need to flip the inequality sign.
(-4x)/(-4) ≤ (-16)/(-4)
x ≤ 4
Step 3: Finally, write the solution in set-builder notation. In this case, since the inequality is less than or equal to, we include the boundary value:
{x | x ≤ 4}
Therefore, the solution to the inequality -4x - 18 ≥ -34 in set-builder notation is {x | x ≤ 4}.
To solve the inequality -4x - 18 ≥ -34, we can begin by isolating the variable, x, on one side of the inequality.
First, we can start by adding 18 to both sides of the inequality:
-4x - 18 + 18 ≥ -34 + 18
This simplifies to:
-4x ≥ -16
Next, to isolate x, we need to divide both sides of the inequality by -4. However, since we are dividing by a negative number, the inequality sign will flip:
-4x/(-4) ≤ -16/(-4)
This simplifies to:
x ≤ 4
Therefore, the solution to the inequality is x ≤ 4.
In set-builder notation, the solution can be written as:
{x | x ≤ 4}