How do you graph an inequality on a number line?
To plot an inequality, such as x>3, on a number line, first draw a circle over the number (e.g., 3). Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in.
Which side do you shade when graphing inequalities?
Shade the top side of the boundary line if you have the inequality symbols > or ≥. Shade the bottom side of the boundary line if you have the inequality symbols < or ≤.
What is a graphing inequality?
When you are graphing inequalities, you will graph the ordinary linear functions just like we done before. The difference is that the solution to the inequality is not the drawn line but the area of the coordinate plane that satisfies the inequality.
What graph represents the inequality y ≥ 2 − 2x?
The graph that represents y≥2−2x, would be the one in the bottom left-hand corner. We know this because the 2 in 2-2x represents the y-intercept and the 2x represents the slope.
How do you write a solution set for an inequality?
Solution Set of an Inequality
- Example: Solve 2x + 3 ≤ 7, where x is a natural number.
- 2x + 3 ≤ 7. Subtracting 3 from both the sides,
- 2x ≤ 4. Dividing both sides by 2,
- x ≤ 2. Since x is a natural number,
- Example: Represent the solution set of inequality x + 4 ≤ 8, where ‘x’ is a whole number.
- x ≤ 4. Since x is a whole number,
- Example 2:
- Solution:
How do you solve inequalities with variables?
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:
- Don’t multiply or divide by a variable (unless you know it is always positive or always negative)
How do you write an inequality interval?
An inequality that includes the boundary point indicated by the “or equal” part of the symbols ≤ ≤ and ≥ ≥ and a closed dot on the number line. The symbol (∞) indicates the interval is unbounded to the right. Express ordering relationships using the symbol < for “less than” and > for “greater than.”
How do you do absolute inequalities?
Use the sign of each side of your inequality to decide which of these cases holds. If the number on the other side of the inequality sign is positive, proceed to step 3….
| Step 1: Isolate the absolute value | |x + 4| – 6 < 9 |x + 4| < 15 |
|---|---|
| Step 4: Solve the compound inequality | -19 < x < 11 |
Can an inequality have infinite solutions?
You can get inequalities that are false for any variable. These inequalities have no solution. You can also get inequalities that are true for any variable. These have an infinite number of solutions.
How do you know when to use and/or or in inequalities?
A compound inequality is just more than one inequality that we want to solve at the same time. We can either use the word ‘and’ or ‘or’ to indicate if we are looking at the solution to both inequalities (and), or if we are looking at the solution to either one of the inequalities (or).
How do you know if a compound inequality has no solution?
If the inequality is greater than a number, we will use OR. If the inequality is less than a number, we will use AND. Remember that if we end up with an absolute value greater than or less than a negative number, there is no solution.
How do you differentiate an inequality?
Note you can never differentiate with an inequality. Instead, the general idea for checking inequalities with differentiation is that we take h(x)=f(x)−g(x) and then try the derivative test to see whether function is increasing or decreasing.
How do you know if a compound inequality is all real numbers?
Solve each inequality separately. The inequality sign is reversed with division by a negative number. Since y could be less than 3 or greater than or equal to −4, y could be any number. The solution is all real numbers.
How do you read an inequality sign?
A closed, or shaded, circle is used to represent the inequalities greater than or equal to (≥) or less than or equal to (≤) . The point is part of the solution. An open circle is used for greater than (>) or less than (<). The point is not part of the solution.
What are the 5 inequality symbols?
These inequality symbols are: less than (<), greater than (>), less than or equal (≤), greater than or equal (≥) and the not equal symbol (≠).
What do inequalities mean in math?
Inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Why do we use inequalities in math?
In mathematics, inequalities are used to compare the relative size of values. They can be used to compare integers, variables, and various other algebraic expressions.