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Section 2.2 Worksheets

PDF Version of these Worksheets

Worksheet Worksheet 1
A4US

1.

Determine the value of \(3x - 5\) when \(x = 4\text{,}\) \(x = 9\text{,}\) and \(x = -5\text{.}\) Write your results as if-then statements.

2.

Solve \(y + c = 7\) for \(y\) using a complete presentation.

3.

Solve \(x^2 + c = 7\) for \(x^2\) using a complete presentation.

4.

Solve the equation \(ax + b = c\) for the variable \(x\) using a complete presentation.

Worksheet Worksheet 2
A4US

1.

Determine the value of \(2x - 5y\) when \(x = 4\) and \(y = 2\text{,}\) and when \(x = 2\text{,}\) and \(y = -3\text{.}\) Write your results as if-then statements.

2.

Check the presentation for errors. If you find one, circle it and describe the mistake in words.

\begin{equation*} \begin{aligned} 2x + 4y \amp = 10 \\ 4y \amp = 2x + 10 \amp \amp \text{Add $2x$ to both sides} \\ y \amp = \frac{2x + 10}{4} \amp \amp \text{Divide both sides by $4$} \\ y \amp = \frac{2x}{4} + \frac{10}{4} \amp \amp \text{Rewrite the fraction} \\ y \amp = \frac{x}{2} + \frac{5}{2} \amp \amp \text{Reduce} \end{aligned} \end{equation*}

3.

Solve the equation \(2x + 3y = 6\) for the variable \(y\) using a complete presentation.

4.

Solve the equation \(2x + 3y = 6\) for the variable \(x\) using a complete presentation.

Worksheet Worksheet 3
A4US

1.

Determine the value of when \(x = 0\text{,}\) \(x = 4\text{,}\) and \(x = -3\text{.}\) Write your results as if-then statements.

2.

Solve \(4x - 3y = 6\) for \(y\) using a complete presentation.

3.

Solve \(ax + by = c\) for \(y\) using a complete presentation.

4.

Work backwards from the given information to derive the original presentation.

\begin{equation*} \begin{aligned} \\ \\ \amp \amp \amp \text{Add $c$ to both sides} \\ \\ a \amp = \frac{b + c}{d} \amp \amp \text{Divide both sides by $d$} \end{aligned} \end{equation*}

Worksheet Worksheet 4
A4US

1.

Determine the value of \(x^2 + 2y^2\) when \(x = -1\) and \(y = 2\text{,}\) and when \(x = -2\) and \(y = -1\text{.}\) Write your results as if-then statements.

2.

Solve \(ax + by = c\) for using a complete presentation.

3.

Solve the equation \(3x - 2y - 4z = 24\) for the variable using a complete presentation.

Worksheet Worksheet 5
A4US

1.

Solve the equation \((x - 5) + a = b\) for the expression \((x - 5)\text{.}\)

2.

Solve the equation \(3 (y + 3) + a = b\) for the expression \((y + 3)\text{.}\)

3.

Work backwards from the given information to derive the original presentation.

\begin{equation*} \begin{aligned} \\ \\ \amp \amp \amp \text{Add 4 to both sides} \\ \\ \amp \amp \amp \text{Divide both sides by 6} \\ \\ \amp \amp \amp \text{Rewrite the fraction} \\ \\ a \amp = \frac{b}{6} + \frac{2}{3} \amp \amp \text{Reduce} \end{aligned} \end{equation*}