Question Solve the inequality $\frac{x}{2} - 3 > 0$ for the real number $x$ .

Studdy Solution

STEP 1

Assumptions1. We are given the inequality $\frac{x}{}-3>0$ . We are assuming that $x$ is a real number

STEP 2

Our goal is to isolate $x$ on one side of the inequality. First, let's add to both sides of the inequality to get rid of the - on the left side.
$\frac{x}{2}-+ >0+$

STEP 3

implify the inequality.
$\frac{x}{2} >3$

STEP 4

To further isolate $x$ , we need to get rid of the fraction. We can do this by multiplying both sides of the inequality by2.
$2 \cdot \frac{x}{2} >2 \cdot3$

STEP 5

implify the inequality.
$x >$ So, the solution to the inequality $\frac{x}{2}-3>0$ is $x >$ .

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Question Solve the inequality $\frac{x}{2} - 3 > 0$ for the real number $x$ .

Studdy Solution

STEP 1

Assumptions1. We are given the inequality $\frac{x}{}-3>0$ . We are assuming that $x$ is a real number

STEP 2

Our goal is to isolate $x$ on one side of the inequality. First, let's add to both sides of the inequality to get rid of the - on the left side.
$\frac{x}{2}-+ >0+$

STEP 3

implify the inequality.
$\frac{x}{2} >3$

STEP 4

To further isolate $x$ , we need to get rid of the fraction. We can do this by multiplying both sides of the inequality by2.
$2 \cdot \frac{x}{2} >2 \cdot3$

STEP 5

implify the inequality.
$x >$ So, the solution to the inequality $\frac{x}{2}-3>0$ is $x >$ .

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Question Solve the inequality x2−3>0\frac{x}{2} - 3 > 02x​−3>0 for the real number xxx.

Studdy Solution

STEP 1

Assumptions1. We are given the inequality x−3>0\frac{x}{}-3>0x​−3>0 . We are assuming that xxx is a real number

STEP 2

Our goal is to isolate xxx on one side of the inequality. First, let's add to both sides of the inequality to get rid of the - on the left side.x2−+>0+\frac{x}{2}-+ >0+2x​−+>0+

STEP 3

implify the inequality.x2>3\frac{x}{2} >32x​>3

STEP 4

To further isolate xxx, we need to get rid of the fraction. We can do this by multiplying both sides of the inequality by2.2⋅x2>2⋅32 \cdot \frac{x}{2} >2 \cdot32⋅2x​>2⋅3

STEP 5

implify the inequality.x>x >x>So, the solution to the inequality x2−3>0\frac{x}{2}-3>02x​−3>0 is x>x >x>.

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Question Solve the inequality $\frac{x}{2} - 3 > 0$ for the real number $x$ .

Assumptions1. We are given the inequality $\frac{x}{}-3>0$ . We are assuming that $x$ is a real number

Our goal is to isolate $x$ on one side of the inequality. First, let's add to both sides of the inequality to get rid of the - on the left side.
$\frac{x}{2}-+ >0+$

implify the inequality.
$\frac{x}{2} >3$

To further isolate $x$ , we need to get rid of the fraction. We can do this by multiplying both sides of the inequality by2.
$2 \cdot \frac{x}{2} >2 \cdot3$

implify the inequality.
$x >$ So, the solution to the inequality $\frac{x}{2}-3>0$ is $x >$ .