What is all real numbers and no solution?
When any and all real numbers substituted in for ‘x’ will satisfy the equation. When the solution has zero in the denominator. When the solution obtained is not true and no value of ‘x’ will satisfy the equation. 2 does not equal 6 so the equation has no solution.
Is 0 0 no solution or all real numbers?
2 Answers. If you end with 0=0 , then it means that the left-hand side and the right-hand side of the equation are equal to each other regardless of the values of the variables involved; therefore, its solution set is all real numbers for each variable.
Does real numbers mean no solution?
If an inequality has no real solution, this means that there are no numbers that can be substituted into the inequality to make the statement true. If an inequality has all real numbers as the solution, this means that every real number can be substituted into the inequality to make a true statement.
How do you know if an inequality has no solution or all real numbers?
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.
What does no real solutions mean?
“No solution” means that there is no value, not even 0, which would satisfy the equation. This is because there is truly no solution—there are no values for x that will make the equation 12 + 2x – 8 = 7x + 5 – 5x true. Example. Problem. Solve for x.
What does all real numbers are solution mean?
To solve an equation means to find all numbers that make the equation true. The numbers are called solutions or roots of the equation. A number that is a solution of an equation is said to satisfy the equation, and the solutions of an equation make up its solution set.
Which inequality has no solution?
Inequalities that produce a false statement have no real solutions. Inequalities that hold true for all values have infinite solutions.
What is an example of no real solution?
For example, the quadratic equation x2 + 4 = 0 has no real solution. In this case, a = 1, b = 0, and c = 4. Since b = 0 when a and c have the same sign (both are positive), we know there is no real solution.
What do we call B² 4ac?
The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
