Algebra: Chapter 9, Lesson 5, page 417.
Inequalities in 2 variables
Given an inequality, treat it as an equality and using the `x` and `y` intercepts, find the solution to the equality. Plot it on your graph paper.
- If the inequality is just a `<`, or `>` problem, then the boundary line (the line you draw connecting the dots) will itself be dotted or dashed. This mean that the points on the line are NOT part of the solution.
- If the inequality has a `≤` or `≥`, then the line will be solid, signifying that the line is part of the solution.
There are 2 ½ planes on the graph, one side of the boundary line that belongs to the solution set (this side will be shaded as part of the solution) and the other side of the line that does not satisfy the inequality.
Now to figure out what ½ plane to shade, pick a point [I like to pick `(0, 0)` or `(1, 1)`] and try those `(x, y)` values in the inequality.
- If the point chosen makes the inequality TRUE, then shade that part of the plane.
- If the point chosen does not satisfy the inequality, then shade the OPPOSITE side ½ plane.
The textbook is actually pretty good in this area, see pages 417-419 for good examples. Purplemath.com has these examples as well.
Two of tonight’s homework problems solved by MrE are here! Just click it
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Algebra 1a: Chapter 3 Review
Skills Practice 8 and 9, pages 16 and 17 AND Mixed Practice #6, page 623.
Make sure that your notes are up-to-date.
Bring your problems worked out and your questions for the Chapter 3 review. These type of questions will appear on the test. Make sure that your notes are up-to-date. Practice makes perfect
Remember how to do the whickity-whack divide thingy.
Remember too, the steps to SOLVING 2-STEP EQUATIONS:
- Multiply both sides to clear fractions or decimals, if necessary.
- Collect like terms on each side, if necessary.
- Use the addition property to move the variable to one side and all other terms to the other side of the equation.
- Collect like terms again, if necessary
- Add or subtract to isolate the variable and finally
- Use the multiplication or division or reciprocal properties to solve for the variable.