Section 10.3 Deliberate Practice: Solving for Variables and Function Expressions
Algebra is a skill, which means it requires practice to become proficient. But it will take more than rote repetition to get there. Deliberate practice is the thoughtful repetition of a task. For each of these sections, you will be given a list of specific skills or ideas to focus on as you practice thinking through the problems.
Focus on these skills:
Write the original expression.
You do not need to use a substitution to replace the function expressions, but it might help.
Avoid inappropriate cancellations and other algebraic errors involving functions.
Present your work legibly.
Worksheet Worksheet
Instructions: Solve for the indicated quantity.
1.
Solve \(\ln(3) x + 5 = \ln(2) x - 7\) for \(x\text{.}\)
2.
Solve \(\pi x + \sqrt{3} = 2x + \cos(2)\) for \(x\text{.}\)
3.
Solve \(\exp(4) x + 3 = \exp(2) x + \exp(5)\) for \(x\text{.}\)
4.
Solve \(\sqrt{5} x - \log(4) = \pi x + \sqrt{7}\) for \(x\text{.}\)
5.
Solve \(2 \sin(x) + \sqrt{3} = 4 \sin(x)\) for \(\sin(x)\text{.}\)
6.
Solve \(5 \cos(x) + \sqrt{2} = 3 \cos(x) - 2\) for \(\cos(x)\text{.}\)
7.
Solve \(4 \ln(x) + 3 = -2 \ln(x) + \ln(4)\) for \(\ln(x)\text{.}\)
8.
Solve \(5 \exp(x) - \sqrt{6} = 2 \exp(x) - \cos(1)\) for \(\exp(x)\text{.}\)
9.
Solve \(3 f(x) - 4 f(2) = g(3) + 6\) for \(f(x)\text{.}\)
10.
Solve \(5 \sqrt{x} + \ln(3) = 4 \exp(2) - 3\) for \(\sqrt{x}\text{.}\)