What is an example of a solution of an inequality?

What is an example of a solution of an inequality?

A “solution” of an inequality is a number which when substituted for the variable makes the inequality a true statement. When we substitute 8 for x, the inequality becomes 8-2 > 5. Thus, x=8 is a solution of the inequality. On the other hand, substituting -2 for x yields the false statement (-2)-2 > 5.

How is an equation and inequality difference?

An equation is a mathematical statement that shows the equal value of two expressions while an inequality is a mathematical statement that shows that an expression is lesser than or more than the other. An equation shows the equality of two variables while an inequality shows the inequality of two variables.

What are the four steps for solving an equation?

We have 4 ways of solving one-step equations: Adding, Substracting, multiplication and division. If we add the same number to both sides of an equation, both sides will remain equal. If we subtract the same number from both sides of an equation, both sides will remain equal.

Is 25 a solution to any inequality?

The number −3 is not included in the solution and that is represented by an open circle on the graph. The inequality x≥6 x ≥ 6 represents all real numbers that are greater than or equal to six. The number six is included in the solution and that is represented by a closed circle on the graph.

Which is a solution to the equation?

A solution to an equation is a value of a variable that makes a true statement when substituted into the equation. The process of finding the solution to an equation is called solving the equation. To find the solution to an equation means to find the value of the variable that makes the equation true.

How many solutions does an inequality have?

infinitely
The solution set of an inequality is the set of all solutions. Typically an inequality has infinitely many solutions and the solution set is easily described using interval notation. The solution set of example 1 is the set of all x <= 7.

What is the golden rule for solving equations?

Do unto one side of the equation, what you do to the other! If we put something on, or take something off of one side, the scale (or equation) is unbalanced.

What are some ways to solve an equation?

A General Rule for Solving Equations

1. Simplify each side of the equation by removing parentheses and combining like terms.
2. Use addition or subtraction to isolate the variable term on one side of the equation.
3. Use multiplication or division to solve for the variable.

What are some differences between equations and inequalities?

One obvious difference between linear equations and inequalities is the solution set. A linear equation of two variables can have more than one solution. For instance, with x = 2_y_ + 3, (5, 1), then (3, 0) and (1, -1) are all solutions to the equation. In each pair, x is the first value and y is the second value.

How do you solve equations with inequalities?

Summary Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. But these things will change direction of the inequality: Multiplying or dividing both sides by a negative number

What are the steps to solving inequalities?

Here are the steps to follow when solving absolute value inequalities: Isolate the absolute value expression on the left side of the inequality. If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions. Remove the absolute value bars by setting up a compound inequality.

What are linear equations and linear inequalities?

The graph of linear inequalities include a dashed line if they are greater than or less than but not equal to. Linear equations, on the other hand, include a solid line in every situation. Moreover, linear inequalities include shaded regions whereas linear equations do not.