Solve For $x$. Your Answer Must Be Simplified.$-12 \leq 44 + X$

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Introduction

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In mathematics, solving for a variable is a fundamental concept that is used to find the value of a variable in an equation. In this article, we will focus on solving for $x$ in the given inequality $-12 \leq 44 + x$. We will use algebraic techniques to isolate the variable $x$ and simplify the expression.

Understanding the Inequality

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The given inequality is $-12 \leq 44 + x$. This means that the value of $x$ must be such that the expression $44 + x$ is greater than or equal to $-12$. To solve for $x$, we need to isolate the variable on one side of the inequality.

Isolating the Variable

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To isolate the variable $x$, we need to get rid of the constant term $44$ on the same side of the inequality. We can do this by subtracting $44$ from both sides of the inequality.

-12 ≤ 44 + x
-12 - 44 ≤ 44 + x - 44
-56 ≤ x

Simplifying the Expression

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Now that we have isolated the variable $x$, we can simplify the expression by combining like terms. In this case, there are no like terms to combine, so the expression remains the same.

Writing the Solution in Interval Notation

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The solution to the inequality $-12 \leq 44 + x$ can be written in interval notation as $[-56, \infty)$. This means that the value of $x$ must be greater than or equal to $-56$.

Conclusion

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In this article, we solved for $x$ in the given inequality $-12 \leq 44 + x$. We used algebraic techniques to isolate the variable $x$ and simplify the expression. The solution to the inequality is $x \geq -56$, which can be written in interval notation as $[-56, \infty)$.

Frequently Asked Questions

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Q: What is the value of $x$ in the inequality $-12 \leq 44 + x$?

A: The value of $x$ is greater than or equal to $-56$.

Q: How do I solve for $x$ in an inequality?

A: To solve for $x$ in an inequality, you need to isolate the variable on one side of the inequality. You can do this by adding or subtracting the same value to both sides of the inequality.

Q: What is the difference between an inequality and an equation?

A: An inequality is a statement that two expressions are not equal, while an equation is a statement that two expressions are equal.

Additional Resources

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• Algebraic Techniques for Solving Inequalities
• Interval Notation
• Solving Inequalities

Step-by-Step Solution

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1. Write down the given inequality: $-12 \leq 44 + x$
2. Subtract $44$ from both sides of the inequality: $-12 - 44 \leq 44 + x - 44$
3. Simplify the expression: $-56 \leq x$
4. Write the solution in interval notation: $[-56, \infty)$

Final Answer

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The final answer is $\boxed{[-56, \infty)}$.

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Introduction

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In our previous article, we solved for $x$ in the given inequality $-12 \leq 44 + x$. We used algebraic techniques to isolate the variable $x$ and simplify the expression. In this article, we will answer some frequently asked questions related to solving for $x$ in inequalities.

Q&A

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Q: What is the difference between an inequality and an equation?

A: An inequality is a statement that two expressions are not equal, while an equation is a statement that two expressions are equal. In an inequality, we use symbols such as $\leq$, $\geq$, $<$, or $>$ to indicate the relationship between the two expressions.

Q: How do I solve for $x$ in an inequality?

A: To solve for $x$ in an inequality, you need to isolate the variable on one side of the inequality. You can do this by adding or subtracting the same value to both sides of the inequality.

Q: What is the order of operations when solving for $x$ in an inequality?

A: The order of operations when solving for $x$ in an inequality is the same as when solving for $x$ in an equation. You need to follow the order of operations (PEMDAS) to evaluate the expression correctly.

Q: Can I use the same methods to solve for $x$ in a linear inequality as I would for a quadratic inequality?

A: No, you cannot use the same methods to solve for $x$ in a linear inequality as you would for a quadratic inequality. Linear inequalities are solved using algebraic techniques, while quadratic inequalities are solved using factoring or the quadratic formula.

Q: How do I write the solution to an inequality in interval notation?

A: To write the solution to an inequality in interval notation, you need to determine the values of $x$ that satisfy the inequality. You can use a number line or a graph to visualize the solution.

Q: Can I use a calculator to solve for $x$ in an inequality?

A: Yes, you can use a calculator to solve for $x$ in an inequality. However, you need to make sure that the calculator is set to the correct mode (e.g., fraction mode) and that you are using the correct operations.

Examples

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Example 1: Solving for $x$ in the inequality $2x + 5 \leq 11$

To solve for $x$ in the inequality $2x + 5 \leq 11$, we need to isolate the variable $x$ on one side of the inequality.

2x + 5 ≤ 11
2x ≤ 11 - 5
2x ≤ 6
x ≤ 6/2
x ≤ 3

The solution to the inequality is $x \leq 3$.

Example 2: Solving for $x$ in the inequality $x - 3 \geq 2$

To solve for $x$ in the inequality $x - 3 \geq 2$, we need to isolate the variable $x$ on one side of the inequality.

x - 3 ≥ 2
x ≥ 2 + 3
x ≥ 5

The solution to the inequality is $x \geq 5$.

Conclusion

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In this article, we answered some frequently asked questions related to solving for $x$ in inequalities. We also provided examples of how to solve for $x$ in linear inequalities. Remember to always follow the order of operations and to isolate the variable $x$ on one side of the inequality.

Frequently Asked Questions

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Q: What is the difference between an inequality and an equation?

A: An inequality is a statement that two expressions are not equal, while an equation is a statement that two expressions are equal.

Q: How do I solve for $x$ in an inequality?

A: To solve for $x$ in an inequality, you need to isolate the variable on one side of the inequality.

Q: What is the order of operations when solving for $x$ in an inequality?

A: The order of operations when solving for $x$ in an inequality is the same as when solving for $x$ in an equation.

Additional Resources

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• Algebraic Techniques for Solving Inequalities
• Interval Notation
• Solving Inequalities

Step-by-Step Solution

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1. Write down the given inequality.
2. Isolate the variable $x$ on one side of the inequality.
3. Simplify the expression.
4. Write the solution in interval notation.

Final Answer

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The final answer is $\boxed{[-56, \infty)}$.