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Section 4.2 Worksheets

PDF Version of these Worksheets

Worksheet Worksheet 1
A4US

1.

Simplify the expression \(2(7a - 4b) - 4(2a - b)\) using a complete presentation. Show the distribution step, the rearrangement step, the grouping step, and the arithmetic step.

2.

Look through your presentation on the previous problem. Which steps do you think can most safely be skipped in terms of demonstrating your understanding? In terms of avoiding errors? Explain your reasoning.

3.

Simplify the expression \(3(x^2 - 2x + 4) - 2(2x^2 + 5)\) using a complete presentation. Show only the steps that you think are the important.

Worksheet Worksheet 2
A4US

1.

Determine whether \(p = -3\) is a solution of the equation \(-2p - 4 = -2\text{.}\)

2.

Solve the equation \(7x = x + 24\) using a complete presentation.

3.

Consider the following presentation for solving the equation from the previous problem.

\begin{equation*} \begin{aligned} 7x \amp = x + 24 \\ 7x - x \amp = x + 24 - x \amp \eqnspacer \amp \text{Subtract $x$ from both sides} \\ 7x - x \amp = x - x + 24 \amp \amp \text{Rearrange the terms} \\ 7x - x \amp = (x - x) + 24 \amp \amp \text{Group the terms} \\ (7 - 1)x \amp = (1 - 1)x + 24 \amp \amp \text{Factor out the $x$} \\ 6x \amp = 0x + 24 \amp \amp \text{Arithmetic} \\ 6x \amp = 24 \amp \amp \text{Simplify} \\ \frac{6x}{6} \amp = \frac{24}{6} \amp \amp \text{Divide both sides by $6$} \\ x \amp = 4 \amp \amp \text{Arithmetic} \end{aligned} \end{equation*}

The work above is all technically correct. Why do you think this would be considered a problematic presentation?

Worksheet Worksheet 3
A4US

1.

Determine whether \(q = -2\) is a solution of the equation \(3q + 1 = -q - 7\text{.}\)

2.

Solve the equation \(3(y + 4) - 2 = 2y - 7\) using a complete presentation.

3.

Solve the equation \(3(2n - 1) + 5 = 4n - 8\) using a complete presentation.

4.

Simplify the expression \(4(a^2 - 2ab + 3b^2) - 3(a^2 + 4ab) - 3(ab + 2b^2)\text{.}\)

Worksheet Worksheet 4
A4US

1.

Verify that \(y = 4\) and \(y = -4\) are both solutions of the equation \(-y^2 + 6 = -10\text{.}\)

2.

For the previous problem, what mistake do you think would be common for students to make?

3.

Solve the equation \(5t + 8 = -3t + 15\) using a complete presentation.

4.

Solve the equation \(-2(s -3) + 2 = 2s + 8\) using a complete presentation.

Worksheet Worksheet 5
A4US

1.

Solve the equation \(5(2a + 7) - 3a + 4 = 3(a - 3) - (2a + 1)\) using a complete presentation.

2.

There is no value of that makes the equation \(3x + 5 = 5(x + 1) - 2x\) false. This means that every choice of the variable will result in a true equation. Attempt to solve the equation using the normal method. Describe what your equation looks like and why it makes sense to conclude that all values of make the equation true.

3.

There is no value of that makes the equation \(-2x + 3 = -2(2x + 1) + 2x\) true. This means that every choice of the variable will result in a false equation. Attempt to solve the equation using the normal method. Describe what your equation looks like and why it makes sense to conclude that all values of make the equation false.