Table of Contents
How do you solve absolute value equations and inequalities?
Key Takeaways
- To solve an absolute value equation, such as |X|=p, replace it with the two equations X=−p and X=p.
- To solve an absolute value inequality involving “less than,” such as |X|≤p, replace it with the compound inequality −p≤X≤p and then solve as usual.
How do you know if an absolute value inequality has no solution?
If the absolute value is less than or less than or equal to a negative number, there is no solution.
How do you know if an absolute value inequality is no solution?
How do you solve an inequality with one variable?
To solve an inequality in one variable, first change it to an equation (a mathematical sentence with an “=” sign) and then solve. Place the solution, called a “boundary point”, on a number line. This point separates the number line into two regions.
What is the example of linear inequality in one variable?
Both sides of an inequality can be multiplied (or divided) by the same positive number. But when both sides are multiplied or divided by a negative number, then the sign of inequality is reversed. For example, 3 > 2 while – 3 < – 2. Also, – 8 < – 7, whereas (– 8)( – 2) > (– 7)( – 2) i.e. 16 > 14.
How do you solve an absolute value equation with one variable?
To solve an equation containing absolute value, isolate the absolute value on one side of the equation. Then set its contents equal to both the positive and negative value of the number on the other side of the equation and solve both equations. Solve | x | + 2 = 5.
What are the 4 steps to solving an absolute value equation?
SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)
- Step 1: Isolate the absolute value expression.
- Step2: Set the quantity inside the absolute value notation equal to + and – the quantity on the other side of the equation.
- Step 3: Solve for the unknown in both equations.
- Step 4: Check your answer analytically or graphically.
How can you tell if an absolute value inequality is all real numbers?
If the absolute value is less than or equal to zero, there is one solution. Just set the argument equal to zero and solve. c. If the absolute value is greater than or equal to zero, the solution is all real numbers.