Algebra 2A Big Ideas 1b
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This is one possible solution for Big Idea 1b.
Step 2
Using the equation in step 1, solve for one variable in terms of the other. For example, solve for b in terms of a like this: b = an expression containing only variable a
Step 3
Write a compound inequality for the area of the rectangle. The area must be greater than 80 and less than 100. The inequality will likely use both variables a and b. The compound inequality will look like this: 80 < expression containing a and b < 100
Step 4
If the expression for area contains both variables a and b, then substitute variable b for the expression found earlier in Step 2. Then the area inequality becomes this:
80 < expression containing only variable a < 100
Step 5
Solve the inequality for variable a. Then use this value to solve for variable b. Then you're done!
Using the equation in step 1, solve for one variable in terms of the other. For example, solve for b in terms of a like this: b = an expression containing only variable a
Step 3
Write a compound inequality for the area of the rectangle. The area must be greater than 80 and less than 100. The inequality will likely use both variables a and b. The compound inequality will look like this: 80 < expression containing a and b < 100
Step 4
If the expression for area contains both variables a and b, then substitute variable b for the expression found earlier in Step 2. Then the area inequality becomes this:
80 < expression containing only variable a < 100
Step 5
Solve the inequality for variable a. Then use this value to solve for variable b. Then you're done!
Did you get stuck with the algebra steps?
When solving the compound inequality the radicals might give you some trouble. Here's an example problem which is not related to this assignment. However it shows what the algebra steps might look like. If you can follow the steps in this example problem, then hopefully you'll be able to go back and solve the inequality in the Big Ideas assignment.
1. Subtract "1" from all three expressions.
2. Divide all three expressions by "2". 3. Take the square root of the three expressions. (Note that taking a square root should result in both positive and negative values. But for the Big Ideas assignment we only care about positive values because the variables represent length values.) |
4. Change the radicals to their decimal form to make the values easier to see.
5. Similar to the Big Ideas assignment, the variable must be *integer* values. We want to answer the question "which integer values are greater than or equal to 2 and less than or equal to 3.16?" We have x = 2 and x = 3 as valid solutions. |