Solved on Jan 23, 2024

Solve the linear inequality $5x/8 \geq 30$ . Graph the solution set.

STEP 1

Assumptions
1. We have the inequality $\frac{5x}{8} \geq 30$ .
2. We need to solve for $x$ .
3. After finding the solution for $x$ , we will graph the solution on a number line.

STEP 2

To solve the inequality $\frac{5x}{8} \geq 30$ , we need to isolate $x$ on one side. We can start by multiplying both sides of the inequality by 8 to eliminate the denominator.
$8 \cdot \frac{5x}{8} \geq 8 \cdot 30$

STEP 3

Simplify both sides of the inequality.
$5x \geq 240$

STEP 4

Now, we divide both sides of the inequality by 5 to solve for $x$ .
$\frac{5x}{5} \geq \frac{240}{5}$

STEP 5

Simplify both sides of the inequality to find the value of $x$ .
$x \geq 48$

STEP 6

To graph the solution, we need to represent all the numbers that are greater than or equal to 48 on a number line.

STEP 7

Draw a number line and mark the point 48 on it.

STEP 8

Since 48 is included in the solution (as indicated by the "greater than or equal to" symbol), we will draw a closed circle at 48 to indicate that it is part of the solution.

STEP 9

Shade the number line to the right of 48 to indicate that all numbers greater than 48 are also part of the solution.
The solution is $x \geq 48$ .

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Solve the linear inequality $5x/8 \geq 30$ . Graph the solution set.

STEP 1

Assumptions
1. We have the inequality $\frac{5x}{8} \geq 30$ .
2. We need to solve for $x$ .
3. After finding the solution for $x$ , we will graph the solution on a number line.

STEP 2

To solve the inequality $\frac{5x}{8} \geq 30$ , we need to isolate $x$ on one side. We can start by multiplying both sides of the inequality by 8 to eliminate the denominator.
$8 \cdot \frac{5x}{8} \geq 8 \cdot 30$

STEP 3

Simplify both sides of the inequality.
$5x \geq 240$

STEP 4

Now, we divide both sides of the inequality by 5 to solve for $x$ .
$\frac{5x}{5} \geq \frac{240}{5}$

STEP 5

Simplify both sides of the inequality to find the value of $x$ .
$x \geq 48$

STEP 6

To graph the solution, we need to represent all the numbers that are greater than or equal to 48 on a number line.

STEP 7

Draw a number line and mark the point 48 on it.

STEP 8

Since 48 is included in the solution (as indicated by the "greater than or equal to" symbol), we will draw a closed circle at 48 to indicate that it is part of the solution.

STEP 9

Shade the number line to the right of 48 to indicate that all numbers greater than 48 are also part of the solution.
The solution is $x \geq 48$ .

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Solve the linear inequality 5x/8≥305x/8 \geq 305x/8≥30. Graph the solution set.

STEP 1

Assumptions1. We have the inequality 5x8≥30\frac{5x}{8} \geq 3085x​≥30.2. We need to solve for xxx.3. After finding the solution for xxx, we will graph the solution on a number line.

STEP 2

To solve the inequality 5x8≥30\frac{5x}{8} \geq 3085x​≥30, we need to isolate xxx on one side. We can start by multiplying both sides of the inequality by 8 to eliminate the denominator.8⋅5x8≥8⋅308 \cdot \frac{5x}{8} \geq 8 \cdot 308⋅85x​≥8⋅30

STEP 3

Simplify both sides of the inequality.5x≥2405x \geq 2405x≥240

STEP 4

Now, we divide both sides of the inequality by 5 to solve for xxx.5x5≥2405\frac{5x}{5} \geq \frac{240}{5}55x​≥5240​

STEP 5

Simplify both sides of the inequality to find the value of xxx.x≥48x \geq 48x≥48

STEP 6

To graph the solution, we need to represent all the numbers that are greater than or equal to 48 on a number line.

STEP 7

Draw a number line and mark the point 48 on it.

STEP 8

Since 48 is included in the solution (as indicated by the "greater than or equal to" symbol), we will draw a closed circle at 48 to indicate that it is part of the solution.

STEP 9

Shade the number line to the right of 48 to indicate that all numbers greater than 48 are also part of the solution.The solution is x≥48x \geq 48x≥48.

Start learning now

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

Solve the linear inequality $5x/8 \geq 30$ . Graph the solution set.

Assumptions
1. We have the inequality $\frac{5x}{8} \geq 30$ .
2. We need to solve for $x$ .
3. After finding the solution for $x$ , we will graph the solution on a number line.

To solve the inequality $\frac{5x}{8} \geq 30$ , we need to isolate $x$ on one side. We can start by multiplying both sides of the inequality by 8 to eliminate the denominator.
$8 \cdot \frac{5x}{8} \geq 8 \cdot 30$

Simplify both sides of the inequality.
$5x \geq 240$

Now, we divide both sides of the inequality by 5 to solve for $x$ .
$\frac{5x}{5} \geq \frac{240}{5}$

Simplify both sides of the inequality to find the value of $x$ .
$x \geq 48$

Shade the number line to the right of 48 to indicate that all numbers greater than 48 are also part of the solution.
The solution is $x \geq 48$ .