QuestionSolve the inequality: $6 - 14x > 11 + 4x$ . Provide your answer as an interval like $[a, oo)$ .

Studdy Solution

STEP 1

Assumptions1. The inequality to solve is $6-14x >11+4x$ . We need to solve for $x$
3. The solution will be presented as an interval

STEP 2

First, we need to isolate $x$ terms on one side of the inequality and constants on the other side. Let's start by subtracting $4x$ from both sides of the inequality.
$6 -14x -4x >11 +4x -4x$

STEP 3

implify the inequality.
$6 -18x >11$

STEP 4

Next, subtract $6$ from both sides of the inequality to isolate the $x$ term on the left side.
$6 -18x -6 >11 -6$

STEP 5

implify the inequality.
$-18x >5$

STEP 6

To solve for $x$ , divide both sides of the inequality by $-18$ . Remember, when we divide or multiply an inequality by a negative number, the direction of the inequality sign changes.
$x < \frac{5}{-18}$

STEP 7

implify the right side of the inequality.
$x < -\frac{5}{18}$ The solution to the inequality $6-14x >11+4x$ is $x < -\frac{5}{18}$ .

STEP 8

We can write the solution as an interval. Since $x$ is less than $-\frac{5}{18}$ , the interval is $(-\infty, -\frac{5}{18})$ .
The solution to the inequality is $x \in (-\infty, -\frac{5}{18})$ .

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