QuestionSolve the inequality $14 > x + 3 > 8$ and graph the solution on a number line.

Studdy Solution

STEP 1

Assumptions1. The inequality is $14 > x +3 >8$ . We are solving for $x$
3. The solution will be a range of values for $x$ that satisfy the inequality

STEP 2

The compound inequality $14 > x + >8$ can be broken down into two separate inequalities1. $14 > x +$
2. $x + >8$

STEP 3

Let's solve the first inequality $14 > x +3$ . We can do this by subtracting3 from both sides of the inequality.
$14 -3 > x +3 -3$

STEP 4

implify the inequality.
$11 > x$

STEP 5

Now, let's solve the second inequality $x +3 >8$ . We can do this by subtracting3 from both sides of the inequality.
$x +3 -3 >8 -3$

STEP 6

implify the inequality.
$x >5$

STEP 7

Now, we combine the two inequalities to get the solution for $x$ .
$11 > x >5$

STEP 8

The solution can be graphed on the number line. $x$ is greater than5 and less than11. So, we mark these two points on the number line and shade the region between them.

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QuestionSolve the inequality $14 > x + 3 > 8$ and graph the solution on a number line.

Studdy Solution

STEP 1

Assumptions1. The inequality is $14 > x +3 >8$ . We are solving for $x$
3. The solution will be a range of values for $x$ that satisfy the inequality

STEP 2

The compound inequality $14 > x + >8$ can be broken down into two separate inequalities1. $14 > x +$
2. $x + >8$

STEP 3

Let's solve the first inequality $14 > x +3$ . We can do this by subtracting3 from both sides of the inequality.
$14 -3 > x +3 -3$

STEP 4

implify the inequality.
$11 > x$

STEP 5

Now, let's solve the second inequality $x +3 >8$ . We can do this by subtracting3 from both sides of the inequality.
$x +3 -3 >8 -3$

STEP 6

implify the inequality.
$x >5$

STEP 7

Now, we combine the two inequalities to get the solution for $x$ .
$11 > x >5$

STEP 8

The solution can be graphed on the number line. $x$ is greater than5 and less than11. So, we mark these two points on the number line and shade the region between them.

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QuestionSolve the inequality 14>x+3>814 > x + 3 > 814>x+3>8 and graph the solution on a number line.

Studdy Solution

STEP 1

Assumptions1. The inequality is 14>x+3>814 > x +3 >814>x+3>8 . We are solving for xxx3. The solution will be a range of values for xxx that satisfy the inequality

STEP 2

The compound inequality 14>x+>814 > x + >814>x+>8 can be broken down into two separate inequalities1. 14>x+14 > x +14>x+2. x+>8x + >8x+>8

STEP 3

Let's solve the first inequality 14>x+314 > x +314>x+3. We can do this by subtracting3 from both sides of the inequality.14−3>x+3−314 -3 > x +3 -314−3>x+3−3

STEP 4

implify the inequality.11>x11 > x11>x

STEP 5

Now, let's solve the second inequality x+3>8x +3 >8x+3>8. We can do this by subtracting3 from both sides of the inequality.x+3−3>8−3x +3 -3 >8 -3x+3−3>8−3

STEP 6

implify the inequality.x>5x >5x>5

STEP 7

Now, we combine the two inequalities to get the solution for xxx.11>x>511 > x >511>x>5

STEP 8

The solution can be graphed on the number line. xxx is greater than5 and less than11. So, we mark these two points on the number line and shade the region between them.

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Studdy solves anything!

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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 $14 > x + 3 > 8$ and graph the solution on a number line.

Assumptions1. The inequality is $14 > x +3 >8$ . We are solving for $x$
3. The solution will be a range of values for $x$ that satisfy the inequality

The compound inequality $14 > x + >8$ can be broken down into two separate inequalities1. $14 > x +$
2. $x + >8$

Let's solve the first inequality $14 > x +3$ . We can do this by subtracting3 from both sides of the inequality.
$14 -3 > x +3 -3$

implify the inequality.
$11 > x$

Now, let's solve the second inequality $x +3 >8$ . We can do this by subtracting3 from both sides of the inequality.
$x +3 -3 >8 -3$

implify the inequality.
$x >5$

Now, we combine the two inequalities to get the solution for $x$ .
$11 > x >5$

The solution can be graphed on the number line. $x$ is greater than5 and less than11. So, we mark these two points on the number line and shade the region between them.