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?

Question

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.

Answer 1

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.

Answer 2

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.