When it comes to linear inequalities, these are explained to be similar to a linear equation, but the difference between the two is that the equal signs are replaced with an inequality symbol. It is also explained that when it comes to doing a linear inequality, it is more complex and there is more to explain and effort that has to be done in order to get your answer.
Linear inequality:If I am correct?
ax+b<0, ax+b<0, ax+b>0, ax+b>0
Each form is unequal to 0
Linear equality system:
4y-2x <20
4y - 2x = 20 is a linear equality.
You are correct in your understanding of linear inequalities. Instead of an equal sign, an inequality symbol is used to compare the two sides of the equation.
To solve a linear inequality, you need to isolate the variable on one side of the inequality symbol. Let's work through your example:
The given linear inequality is 4y - 2x < 20.
Step 1: To start isolating the variable, let's move the constant term (20) to the other side of the inequality by adding or subtracting it from both sides:
4y - 2x - 20 < 0
Step 2: Next, we want to isolate the variable terms. In this case, we have -2x and 4y on the left side. To isolate the variable, let's move the -2x term to the right side by adding 2x to both sides:
4y - 20 < 2x
Step 3: Now, we want to express the inequality in terms of a single variable. Let's divide both sides of the inequality by 2:
(4y - 20)/2 < x
Simplifying further, we have:
2y - 10 < x
So, the solved linear inequality is 2y - 10 < x.
Remember that the solution to a linear inequality is not a single value, but rather a range of values that satisfy the inequality. You can graph the inequality on a coordinate plane or substitute different values in order to visualize and identify the set of values that satisfy the inequality.
I hope this explanation helps! Let me know if you have any further questions.