Solve The Inequity And Show The Graph Of The Solution 5x_<7x+22
Introduction
Inequalities are mathematical expressions that compare two values using greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤) symbols. Solving inequalities involves finding the values of the variable that make the inequality true. In this article, we will focus on solving the inequality 5x < 7x + 22.
Understanding the Inequality
The given inequality is 5x < 7x + 22. To solve this inequality, we need to isolate the variable x. We can start by subtracting 5x from both sides of the inequality.
Subtracting 5x from Both Sides
5x - 5x < 7x + 22 - 5x
0 < 2x + 22
Isolating the Variable
Next, we need to isolate the variable x. We can do this by subtracting 22 from both sides of the inequality.
Subtracting 22 from Both Sides
0 - 22 < 2x + 22 - 22
-22 < 2x
Dividing Both Sides by 2
Finally, we need to divide both sides of the inequality by 2 to solve for x.
Dividing Both Sides by 2
-22/2 < 2x/2
-11 < x
Graphing the Solution
The solution to the inequality is x < -11. We can graph this solution on a number line.
Graphing the Solution on a Number Line
-15 | -14 | -13 | -12 | -11 | -10
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**Solving Inequalities: A Step-by-Step Guide**
=====================================================
Q&A: Solving Inequalities
Q: What is an inequality?
A: An inequality is a mathematical expression that compares two values using greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤) symbols.
Q: How do I solve an inequality?
A: To solve an inequality, you need to isolate the variable by performing operations on both sides of the inequality. You can add, subtract, multiply, or divide both sides of the inequality, but you must do the same operation to both sides.
Q: What is the difference between solving an equation and solving an inequality?
A: Solving an equation involves finding the value of the variable that makes the equation true, whereas solving an inequality involves finding the values of the variable that make the inequality true.
Q: Can I use the same steps to solve all types of inequalities?
A: No, the steps to solve different types of inequalities may vary. For example, to solve a linear inequality, you can use the same steps as solving a linear equation. However, to solve a quadratic inequality, you may need to use different methods, such as factoring or using the quadratic formula.
Q: How do I graph the solution to an inequality?
A: To graph the solution to an inequality, you can use a number line or a coordinate plane. For example, if the inequality is x < 3, you can graph a line at x = 3 and shade the region to the left of the line.
Q: Can I use a calculator to solve an inequality?
A: Yes, you can use a calculator to solve an inequality, but you need to be careful when using a calculator to solve an inequality. Some calculators may not be able to handle inequalities, and you may need to use a different calculator or method to solve the inequality.
Q: How do I check my solution to an inequality?
A: To check your solution to an inequality, you can plug the value of the variable back into the original inequality and see if it is true. If the inequality is true, then your solution is correct.
Q: Can I solve an inequality with fractions?
A: Yes, you can solve an inequality with fractions. To do this, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as multiplying both sides of the inequality by the least common multiple of the denominators.
Q: How do I solve an inequality with absolute value?
A: To solve an inequality with absolute value, you need to consider two cases: when the expression inside the absolute value is positive and when it is negative. You can then use the same steps as solving an inequality to solve each case.
Q: Can I solve an inequality with exponents?
A: Yes, you can solve an inequality with exponents. To do this, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as using the properties of exponents.
Q: How do I solve an inequality with radicals?
A: To solve an inequality with radicals, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as using the properties of radicals.
Q: Can I solve an inequality with a variable in the denominator?
A: Yes, you can solve an inequality with a variable in the denominator. To do this, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as multiplying both sides of the inequality by the denominator.
Q: How do I solve an inequality with a fraction in the numerator?
A: To solve an inequality with a fraction in the numerator, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as multiplying both sides of the inequality by the denominator.
Q: Can I solve an inequality with a negative number?
A: Yes, you can solve an inequality with a negative number. To do this, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as multiplying both sides of the inequality by -1.
Q: How do I solve an inequality with a decimal number?
A: To solve an inequality with a decimal number, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as multiplying both sides of the inequality by a power of 10.
Q: Can I solve an inequality with a mixed number?
A: Yes, you can solve an inequality with a mixed number. To do this, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as converting the mixed number to an improper fraction.
Q: How do I solve an inequality with a variable in the exponent?
A: To solve an inequality with a variable in the exponent, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as using the properties of exponents.
Q: Can I solve an inequality with a radical in the exponent?
A: Yes, you can solve an inequality with a radical in the exponent. To do this, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as using the properties of radicals.
Q: How do I solve an inequality with a variable in the denominator and a radical in the numerator?
A: To solve an inequality with a variable in the denominator and a radical in the numerator, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as multiplying both sides of the inequality by the denominator and then using the properties of radicals.
Q: Can I solve an inequality with a negative number in the denominator?
A: Yes, you can solve an inequality with a negative number in the denominator. To do this, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as multiplying both sides of the inequality by -1.
Q: How do I solve an inequality with a decimal number in the denominator?
A: To solve an inequality with a decimal number in the denominator, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as multiplying both sides of the inequality by a power of 10.
Q: Can I solve an inequality with a mixed number in the denominator?
A: Yes, you can solve an inequality with a mixed number in the denominator. To do this, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as converting the mixed number to an improper fraction.
Q: How do I solve an inequality with a variable in the exponent and a radical in the numerator?
A: To solve an inequality with a variable in the exponent and a radical in the numerator, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as using the properties of exponents and radicals.
Q: Can I solve an inequality with a negative number in the exponent?
A: Yes, you can solve an inequality with a negative number in the exponent. To do this, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as using the properties of exponents.
Q: How do I solve an inequality with a decimal number in the exponent?
A: To solve an inequality with a decimal number in the exponent, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as multiplying both sides of the inequality by a power of 10.
Q: Can I solve an inequality with a mixed number in the exponent?
A: Yes, you can solve an inequality with a mixed number in the exponent. To do this, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as converting the mixed number to an improper fraction.
Q: How do I solve an inequality with a variable in the denominator and a radical in the numerator and a negative number in the exponent?
A: To solve an inequality with a variable in the denominator and a radical in the numerator and a negative number in the exponent, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as multiplying both sides of the inequality by the denominator, then using the properties of radicals and exponents.
Q: Can I solve an inequality with a negative number in the denominator and a radical in the numerator and a negative number in the exponent?
A: Yes, you can solve an inequality with a negative number in the denominator and a radical in the numerator and a negative number in the exponent. To do this, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as multiplying both sides of the inequality by -1, then using the properties of radicals and exponents.
Q: How do I solve an inequality with a decimal number in the denominator and a radical in the numerator and a negative number in the exponent?
A: To solve an inequality with a decimal number in the denominator and a radical in the numerator and a negative number in the exponent, you need to follow the same steps as solving an inequality with integers, but you may need to use different methods, such as multiplying both sides of the inequality by a power of 10, then using the properties of radicals and exponents.
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