Can anyone help me with dq i week 2Post your response to the following: How do you know if a value is a solution for an inequality? How is this different from determining if a value is a solution to an equation?
If you replace the equal sign of an equation with an inequality sign, is there ever a time when the same value will be a solution to both the equation and the inequality?
Write an inequality and provide a value that may or may not be a solution to the inequality. I don't understand it Thank you in advance.
Inequalities are solved the same way as equations, except that the carat (<) is reversed when multiplying both sides by a negative number.
-4x > 8
x < -2
I hope this helps.
Y > X -2. Write and graph Eq of boundry
line: Y = X -2, (0, -2), (2, 0), (4 ,2)
The Eq of the boundary line always uses an equal sign. However,since there is no = sign in your original in-
equality,the graph should be a dotted line. The points on the dotted line
should not satisfy the inequality:
Y > X - 2
-2 > 0 -2
-2 > -2, This is not a true statement.
Therefore, the point does not satisfy the inequality and not a solution.
Let's test a point above the line:(0,0).
Y > X - 2
0 > 0 - 2
0 > -2, This is a true statement and
a solution. If 1 point above the line
is a solution, then all points above
the line are solutions. None of the
points below the line are solutions;
and , therefore, do not satisfy the
inequality. TEST A FEW!
If your inequality contained an =
sign(X - Y >= -2), your boundary
line would be a solid line, and all
points on it would satisfy the in-
equality.
An equation states that the
quanity on the left is equal to the
quantity on the right. So if I replace
the equal sign with an inequality sign, it becomes an untrue statement;
because it is still an equation.
To determine if a value is a solution for an inequality, you can substitute the value into the inequality and see if the resulting inequality is true. For example, if the inequality is x > 5, you would substitute a specific value for x, such as 6, and check if the statement 6 > 5 is true. If it is true, then 6 is a solution for the inequality.
This differs from determining if a value is a solution to an equation because equations use the equal sign rather than an inequality sign. In equations, you substitute the value into the equation and check if the resulting equation is true. For example, if the equation is x + 3 = 9, you would substitute a specific value for x, such as 6, and check if the statement 6 + 3 = 9 is true. If it is true, then 6 is a solution for the equation.
There can be instances where the same value is a solution to both an equation and an inequality. For example, if the equation is x = 5 and the inequality is x ≥ 5, both the equation and the inequality would have 5 as a solution.
Let's take an example of an inequality: 2x + 3 > 7. To determine if a value is a solution, you can substitute a value for x and see if the resulting inequality is true. Let's substitute x = 2: 2(2) + 3 > 7. Simplifying this, we get 4 + 3 > 7 which is true. So, x = 2 is a possible solution for the inequality 2x + 3 > 7.
To determine if a value is a solution for an inequality, you need to substitute the value into the inequality and see if it satisfies the inequality. If the value makes the inequality true, then it is a solution. For example, if you have the inequality x > 5 and you want to check if x = 6 is a solution, you would substitute x = 6 into the inequality: 6 > 5. Since this statement is true, 6 is indeed a solution to the inequality.
On the other hand, to determine if a value is a solution for an equation, you substitute that value into the equation and check if both sides of the equation are equal. If they are, then the value is a solution to the equation. For example, if you have the equation x = 5 and you want to check if x = 6 is a solution, you would substitute x = 6 into the equation: 6 = 5. Since this statement is false, 6 is not a solution to the equation.
When you replace the equal sign of an equation with an inequality sign, there can be instances where the same value is a solution to both the equation and the inequality. For example, if you have the equation x = 5 and you replace the equal sign with a greater than sign to create the inequality x > 5, then x = 5 would satisfy both the equation and the inequality because 5 is indeed greater than 5.
As for writing an inequality and providing a value that may or may not be a solution, let's consider the inequality 2x + 3 < 10. To check if x = 2 is a solution, substitute x = 2 into the inequality: 2(2) + 3 < 10. This simplifies to 7 < 10, which is true. Therefore, x = 2 is a solution to the inequality.