Section 2.3 Deliberate Practice: Solving Equations for a Variable Expression
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 equation.
Line up your equal signs.
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Correctly state the algebraic steps using the correct phrasing:
Add (expression) to both sides.
Subtract (expression) from both sides.
Multiply both sides by (expression).
Divide both sides by (expression).
Execute the algebra and arithmetic correctly.
Present your work legibly.
Worksheet Worksheet
Instructions: Solve the equations for the variable expression using a complete presentation.
1.
Solve \(6x^2 + 23 = 41\) for the expression \(x^2\text{.}\)
2.
Solve \(2y^3 + 14 = -20\) for the expression \(y^3\text{.}\)
3.
Solve \(5(t - 5) - 7 = 7\) for the expression \((t-5)\text{.}\)
4.
Solve \(6(r + 8) - 18 = 53\) for the expression \((r+8)\text{.}\)
5.
Solve \(3(b^2 + 4) - 25 = -38\) for the expression \((b^2 + 4)\text{.}\)
6.
Solve \(2x^2 + 4y^2 + 3z^2 + 5 = 11\) for the expression \(x^2\text{.}\)
7.
Solve \(2x^2 + 4y^2 + 3z^2 + 5 = 11\) for the expression \(y^2\text{.}\)
8.
Solve \(2x^2 + 4y^2 + 3z^2 + 5 = 11\) for the expression \(z^2\text{.}\)
9.
Solve \(4\ln(x) + 7 = 22\) for the expression \(\ln(x)\text{.}\)
10.
Solve \(3 \sin(2x) + 8 = 14\) for the expression \(\sin(2x)\text{.}\)