The correct step is to subtract 3 from both sides

Oct 13, 2025 by leolavanderia.com.br 63 views

Understanding the Basics of Inequality Solving

When it comes to solving inequalities, the first step is crucial in determining the correct solution. Inequality solving involves isolating the variable, which in this case is x. The given inequality is $2x + 3 \geq 17$ . To solve this, we need to follow a series of steps that will help us isolate the variable x.

Isolating the Variable

The first step in solving the inequality $2x + 3 \geq 17$ is to isolate the variable x. This can be achieved by subtracting 3 from both sides of the inequality. However, before we proceed with this step, let's understand the concept of isolating the variable.

Isolating the variable means getting the variable x by itself on one side of the inequality. This can be done by performing operations on both sides of the inequality. In this case, we need to get rid of the constant term 3 that is being added to the variable x.

Why Subtracting 3 from Both Sides is the Correct Step

Subtracting 3 from both sides of the inequality is the correct step because it allows us to isolate the variable x. By subtracting 3 from both sides, we are effectively getting rid of the constant term 3 that is being added to the variable x.

The correct step is to subtract 3 from both sides because it allows us to isolate the variable x. This is the first step in solving the inequality $2x + 3 \geq 17$ .

What Happens if We Divide the Left Side by 2?

If we divide the left side of the inequality by 2, we will be changing the direction of the inequality. This is because dividing both sides of an inequality by a negative number changes the direction of the inequality.

Dividing the left side by 2 is not the correct step because it changes the direction of the inequality. This is not what we want to do when solving the inequality $2x + 3 \geq 17$ .

What Happens if We Change the Direction of the Inequality?

If we change the direction of the inequality, we will be changing the solution set of the inequality. This is because changing the direction of the inequality changes the relationship between the variable x and the constant term.

Changing the direction of the inequality is not the correct step because it changes the solution set of the inequality. This is not what we want to do when solving the inequality $2x + 3 \geq 17$ .

What Happens if We Change the Inequality to $\textgreater$ ?

If we change the inequality to $\textgreater$ , we will be changing the direction of the inequality. This is because changing the inequality to $\textgreater$ changes the relationship between the variable x and the constant term.

Changing the inequality to $\textgreater$ is not the correct step because it changes the direction of the inequality. This is not what we want to do when solving the inequality $2x + 3 \geq 17$ .

Conclusion

In conclusion, the first step in solving the inequality $2x + 3 \geq 17$ is to subtract 3 from both sides. This allows us to isolate the variable x and get rid of the constant term 3 that is being added to the variable x. Dividing the left side by 2, changing the direction of the inequality, and changing the inequality to $\textgreater$ are not the correct steps because they change the direction of the inequality or the solution set of the inequality.

Final Answer

The final answer is: B. Subtract 3 from both sides.

Step-by-Step Solution

Here is the step-by-step solution to the inequality $2x + 3 \geq 17$ :

Subtract 3 from both sides of the inequality: $2x + 3 - 3 \geq 17 - 3$
Simplify the inequality: $2x \geq 14$
Divide both sides of the inequality by 2: $\frac{2x}{2} \geq \frac{14}{2}$
Simplify the inequality: $x \geq 7$

The final answer is $x \geq 7$ .

Understanding Inequality Solving

Solving inequalities involves isolating the variable, which in this case is x. The given inequality is $2x + 3 \geq 17$ . To solve this, we need to follow a series of steps that will help us isolate the variable x.

Q&A Session

Q: What is the first step in solving the inequality $2x + 3 \geq 17$ ?

A: The first step in solving the inequality $2x + 3 \geq 17$ is to subtract 3 from both sides of the inequality. This allows us to isolate the variable x and get rid of the constant term 3 that is being added to the variable x.

Q: Why is subtracting 3 from both sides the correct step?

A: Subtracting 3 from both sides is the correct step because it allows us to isolate the variable x. By subtracting 3 from both sides, we are effectively getting rid of the constant term 3 that is being added to the variable x.

Q: What happens if we divide the left side by 2?

A: If we divide the left side of the inequality by 2, we will be changing the direction of the inequality. This is because dividing both sides of an inequality by a negative number changes the direction of the inequality.

Q: What happens if we change the direction of the inequality?

A: If we change the direction of the inequality, we will be changing the solution set of the inequality. This is because changing the direction of the inequality changes the relationship between the variable x and the constant term.

Q: What happens if we change the inequality to $\textgreater$ ?

A: If we change the inequality to $\textgreater$ , we will be changing the direction of the inequality. This is because changing the inequality to $\textgreater$ changes the relationship between the variable x and the constant term.

Q: How do we solve the inequality $2x + 3 \geq 17$ ?

A: To solve the inequality $2x + 3 \geq 17$ , we need to follow these steps:

Subtract 3 from both sides of the inequality: $2x + 3 - 3 \geq 17 - 3$
Simplify the inequality: $2x \geq 14$
Divide both sides of the inequality by 2: $\frac{2x}{2} \geq \frac{14}{2}$
Simplify the inequality: $x \geq 7$

Q: What is the final answer to the inequality $2x + 3 \geq 17$ ?

A: The final answer to the inequality $2x + 3 \geq 17$ is $x \geq 7$ .

Conclusion

In conclusion, solving inequalities involves isolating the variable, which in this case is x. The first step in solving the inequality $2x + 3 \geq 17$ is to subtract 3 from both sides of the inequality. This allows us to isolate the variable x and get rid of the constant term 3 that is being added to the variable x.

Final Tips

Always follow the order of operations when solving inequalities.
Make sure to isolate the variable x by getting rid of any constant terms that are being added to or subtracted from the variable x.
Be careful when dividing both sides of an inequality by a negative number, as this will change the direction of the inequality.

Common Mistakes to Avoid

Dividing both sides of an inequality by a negative number without changing the direction of the inequality.
Changing the direction of the inequality without changing the solution set of the inequality.
Failing to isolate the variable x by getting rid of any constant terms that are being added to or subtracted from the variable x.

Final Answer

The final answer is: $x \geq 7$ .