Solve The Inequality For W W W . W + 14 ≤ − 7 W + 14 \leq -7 W + 14 ≤ − 7 Simplify Your Answer As Much As Possible. □ \square □

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Introduction


Linear inequalities are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific type of linear inequality, which is the inequality w+147w + 14 \leq -7. Our goal is to isolate the variable ww and simplify the inequality as much as possible.

Understanding Linear Inequalities


Before we dive into solving the inequality, let's take a moment to understand what linear inequalities are. A linear inequality is an inequality that involves a linear expression, which is an expression that can be written in the form ax+bax + b, where aa and bb are constants and xx is a variable. Linear inequalities can be written in the form ax+bcax + b \leq c or ax+bcax + b \geq c, where cc is a constant.

Solving the Inequality


Now that we have a basic understanding of linear inequalities, let's focus on solving the inequality w+147w + 14 \leq -7. To solve this inequality, we need to isolate the variable ww. We can do this by subtracting 14 from both sides of the inequality.

Step 1: Subtract 14 from Both Sides


When we subtract 14 from both sides of the inequality, we get:

w+1414714w + 14 - 14 \leq -7 - 14

This simplifies to:

w21w \leq -21

Step 2: Simplify the Inequality


Now that we have isolated the variable ww, we can simplify the inequality by writing it in the form w21w \leq -21. This is the final solution to the inequality.

Conclusion


Solving linear inequalities is an important skill for students to master. By following the steps outlined in this article, we can solve the inequality w+147w + 14 \leq -7 and simplify it to w21w \leq -21. Remember to always isolate the variable and simplify the inequality as much as possible.

Tips and Tricks


Here are some tips and tricks to help you solve linear inequalities:

  • Always isolate the variable by adding or subtracting the same value from both sides of the inequality.
  • Simplify the inequality by writing it in the form ax+bcax + b \leq c or ax+bcax + b \geq c.
  • Use inverse operations to isolate the variable. For example, if the inequality involves a multiplication or division operation, use the inverse operation to isolate the variable.

Examples


Here are some examples of linear inequalities that you can try to solve:

  • x+510x + 5 \leq 10
  • y32y - 3 \geq 2
  • z+21z + 2 \leq -1

Practice Problems


Here are some practice problems to help you practice solving linear inequalities:

  • Solve the inequality x+25x + 2 \leq 5.
  • Solve the inequality y13y - 1 \geq 3.
  • Solve the inequality z+12z + 1 \leq -2.

Final Thoughts


Solving linear inequalities is an important skill for students to master. By following the steps outlined in this article and practicing with examples and practice problems, you can become proficient in solving linear inequalities. Remember to always isolate the variable and simplify the inequality as much as possible.

References


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Introduction


In our previous article, we discussed how to solve linear inequalities, with a focus on the inequality w+147w + 14 \leq -7. We learned how to isolate the variable ww and simplify the inequality. In this article, we will answer some common questions that students often have when it comes to solving linear inequalities.

Q&A


Q: What is a linear inequality?

A: A linear inequality is an inequality that involves a linear expression, which is an expression that can be written in the form ax+bax + b, where aa and bb are constants and xx is a variable.

Q: How do I solve a linear inequality?

A: To solve a linear inequality, you need to isolate the variable by adding or subtracting the same value from both sides of the inequality. You can also use inverse operations to isolate the variable.

Q: What is the difference between a linear inequality and a linear equation?

A: A linear equation is an equation that involves a linear expression, whereas a linear inequality is an inequality that involves a linear expression. In other words, a linear equation is a statement that two expressions are equal, whereas a linear inequality is a statement that one expression is greater than, less than, or equal to another expression.

Q: Can I use the same methods to solve a linear inequality as I would to solve a linear equation?

A: Yes, you can use the same methods to solve a linear inequality as you would to solve a linear equation. However, you need to be careful when using inverse operations, as they may change the direction of the inequality.

Q: How do I know which direction to write the inequality?

A: When solving a linear inequality, you need to determine which direction to write the inequality. If the inequality is in the form ax+bcax + b \leq c, you will write the inequality as xcbax \leq \frac{c-b}{a}. If the inequality is in the form ax+bcax + b \geq c, you will write the inequality as xcbax \geq \frac{c-b}{a}.

Q: Can I use a calculator to solve a linear inequality?

A: Yes, you can use a calculator to solve a linear inequality. However, you need to be careful when using a calculator, as it may not always give you the correct solution.

Q: How do I check my solution to a linear inequality?

A: To check your solution to a linear inequality, you need to plug the solution back into the original inequality and see if it is true. If the solution is true, then you have found the correct solution.

Examples


Here are some examples of linear inequalities that you can try to solve:

  • x+510x + 5 \leq 10
  • y32y - 3 \geq 2
  • z+21z + 2 \leq -1

Practice Problems


Here are some practice problems to help you practice solving linear inequalities:

  • Solve the inequality x+25x + 2 \leq 5.
  • Solve the inequality y13y - 1 \geq 3.
  • Solve the inequality z+12z + 1 \leq -2.

Conclusion


Solving linear inequalities is an important skill for students to master. By following the steps outlined in this article and practicing with examples and practice problems, you can become proficient in solving linear inequalities. Remember to always isolate the variable and simplify the inequality as much as possible.

Tips and Tricks


Here are some tips and tricks to help you solve linear inequalities:

  • Always isolate the variable by adding or subtracting the same value from both sides of the inequality.
  • Simplify the inequality by writing it in the form ax+bcax + b \leq c or ax+bcax + b \geq c.
  • Use inverse operations to isolate the variable.
  • Check your solution to a linear inequality by plugging the solution back into the original inequality.

References