QuestionSolve the inequality: $\frac{3 x-7}{-3}>7$ . Provide the solution set in interval notation and graph form.

Studdy Solution

STEP 1

Assumptions1. We are solving the inequality $\frac{3x -7}{-3} >7$ . . The solution set is the set of all real numbers x that satisfy the inequality.
3. The inequality is strict, meaning that the solution set does not include the values where the expression equals7.

STEP 2

First, we can simplify the inequality by multiplying both sides by -. Note that when we multiply or divide an inequality by a negative number, the direction of the inequality sign changes.
$x -7 < -21$

STEP 3

Next, we can isolate the variable x by adding7 to both sides of the inequality.
$3x < -14$

STEP 4

Finally, we can solve for x by dividing both sides of the inequality by3.
$x < -\frac{14}{3}$

STEP 5

Now we have the solution set in interval notation. The interval notation for $x < -\frac{14}{3}$ is $(-\infty, -\frac{14}{3})$ . This means that the solution set includes all real numbers less than $-\frac{14}{3}$ .
The solution set is $(-\infty, -\frac{14}{3})$ .

STEP 6

To represent the solution set on a graph, we draw a number line and mark the point $-\frac{14}{3}$ . Because the inequality is strict (x is less than $-\frac{14}{3}$ ), we use an open circle to indicate that $-\frac{14}{3}$ is not included in the solution set. Then, we draw an arrow to the left of $-\frac{14}{3}$ to represent all real numbers less than $-\frac{14}{3}$ .
The solution set in graph form is an open circle at $-\frac{14}{3}$ with an arrow pointing to the left.

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QuestionSolve the inequality: $\frac{3 x-7}{-3}>7$ . Provide the solution set in interval notation and graph form.

Studdy Solution

STEP 1

Assumptions1. We are solving the inequality $\frac{3x -7}{-3} >7$ . . The solution set is the set of all real numbers x that satisfy the inequality.
3. The inequality is strict, meaning that the solution set does not include the values where the expression equals7.

STEP 2

First, we can simplify the inequality by multiplying both sides by -. Note that when we multiply or divide an inequality by a negative number, the direction of the inequality sign changes.
$x -7 < -21$

STEP 3

Next, we can isolate the variable x by adding7 to both sides of the inequality.
$3x < -14$

STEP 4

Finally, we can solve for x by dividing both sides of the inequality by3.
$x < -\frac{14}{3}$

STEP 5

Now we have the solution set in interval notation. The interval notation for $x < -\frac{14}{3}$ is $(-\infty, -\frac{14}{3})$ . This means that the solution set includes all real numbers less than $-\frac{14}{3}$ .
The solution set is $(-\infty, -\frac{14}{3})$ .

STEP 6

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QuestionSolve the inequality: 3x−7−3>7\frac{3 x-7}{-3}>7−33x−7​>7. Provide the solution set in interval notation and graph form.

Studdy Solution

STEP 1

Assumptions1. We are solving the inequality 3x−7−3>7\frac{3x -7}{-3} >7−33x−7​>7. . The solution set is the set of all real numbers x that satisfy the inequality.3. The inequality is strict, meaning that the solution set does not include the values where the expression equals7.

STEP 2

First, we can simplify the inequality by multiplying both sides by -. Note that when we multiply or divide an inequality by a negative number, the direction of the inequality sign changes.x−7<−21x -7 < -21x−7<−21

STEP 3

Next, we can isolate the variable x by adding7 to both sides of the inequality.3x<−143x < -143x<−14

STEP 4

Finally, we can solve for x by dividing both sides of the inequality by3.x<−143x < -\frac{14}{3}x<−314​

STEP 5

STEP 6

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the inequality: $\frac{3 x-7}{-3}>7$ . Provide the solution set in interval notation and graph form.

Assumptions1. We are solving the inequality $\frac{3x -7}{-3} >7$ . . The solution set is the set of all real numbers x that satisfy the inequality.
3. The inequality is strict, meaning that the solution set does not include the values where the expression equals7.

First, we can simplify the inequality by multiplying both sides by -. Note that when we multiply or divide an inequality by a negative number, the direction of the inequality sign changes.
$x -7 < -21$

Next, we can isolate the variable x by adding7 to both sides of the inequality.
$3x < -14$

Finally, we can solve for x by dividing both sides of the inequality by3.
$x < -\frac{14}{3}$