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Teacherbot 15 Sep, 18:47:59

1) To solve inequalities, you need to isolate the variable on one side of the inequality sign. You can do this by performing the same operations on both sides of the inequality sign, just like in equations. However, there are a few additional rules to keep in mind when solving inequalities:

  • If you multiply or divide both sides of the inequality by a negative number, you must reverse the direction of the inequality sign.
  • If you add or subtract the same number from both sides of the inequality, the direction of the inequality sign remains the same.

For example, let’s solve the inequality 2x + 5 > 10:

First, subtract 5 from both sides: 2x > 5

Then, divide both sides by 2: x > 2.5

So the solution to the inequality is x > 2.5.

2) When you have variables on both sides of the inequality sign, you need to collect all the variable terms on one side and all the constant terms on the other side. Then, you can solve the inequality as usual.

For example, let’s solve the inequality 3x + 4 < 2x + 7:

First, subtract 2x from both sides: x + 4 < 7

Then, subtract 4 from both sides: x < 3

So the solution to the inequality is x < 3.

3) Inequalities can have infinitely many solutions or no solutions at all. This depends on the relationship between the variables and the inequality sign.

  • If the inequality is always true, regardless of the value of the variable, then it has infinitely many solutions. For example, the inequality x > x + 1 has no solution because it is never true for any value of x.

  • If the inequality is always false, regardless of the value of the variable, then it has no solution. For example, the inequality 2x > 2x + 1 has no solution because it is never true for any value of x.

4) Inequalities can be used to solve various types of problems, such as word problems involving quantities that are greater than or less than certain values. For example, if you have a problem that states “The sum of two numbers is at least 10,” you can represent this as an inequality: x + y ≥ 10, where x and y are the two numbers. By solving this inequality, you can find the range of possible values for x and y that satisfy the given condition.

You 15 Sep, 18:49:09

Make this simpler to understand

Teacherbot 15 Sep, 18:49:09

1) To solve inequalities, you need to isolate the variable on one side of the inequality sign. You can do this by performing the same operations on both sides of the inequality sign, just like in equations.

2) When you have variables on both sides of the inequality sign, you need to collect all the variable terms on one side and all the constant terms on the other side. Then, you can solve the inequality as usual.

3) Inequalities can have infinitely many solutions or no solutions at all. This depends on the relationship between the variables and the inequality sign.

  • If the inequality is always true, regardless of the value of the variable, then it has infinitely many solutions.
  • If the inequality is always false, regardless of the value of the variable, then it has no solution.

4) Inequalities can be used to solve various types of problems, such as word problems involving quantities that are greater than or less than certain values. By solving the inequality, you can find the range of possible values that satisfy the given condition.