Example 1
Completion requirements
| Example 1 |
Solve the inequality \(2d - 2 \lt 3d + 2\). Show the solution set on a number line. Use a value of the solution set to verify the solution.
\(\begin{align}
2d - 2 &< 3d + 2 \\
- d &< 4 \\
d &> - 4 \\
\end{align}\)
The solution set is {\(d|d \gt -4, \thinspace d \in \rm{R}\)}.
The solution can be verified using any value that lies on the red number line. A verification of the solution to an inequality does not guarantee the solution is correct, but it may show that the solution is incorrect. The following verification uses the value \(–1\).
The left side is less than the right side, so this verification does not show an error.
2d - 2 &< 3d + 2 \\
- d &< 4 \\
d &> - 4 \\
\end{align}\)
The solution set is {\(d|d \gt -4, \thinspace d \in \rm{R}\)}.
The solution can be verified using any value that lies on the red number line. A verification of the solution to an inequality does not guarantee the solution is correct, but it may show that the solution is incorrect. The following verification uses the value \(–1\).
| Left Side | Right Side |
|---|---|
|
\(\begin{array}{r} 2d - 2 \\ 2\left( { - 1} \right) - 2 \\ - 4 \end{array}\) |
\(\begin{array}{l} 3d + 2 \\ 3\left( { - 1} \right) + 2 \\ - 1 \end{array}\) |
| LS \(\lt \) RS | |
The left side is less than the right side, so this verification does not show an error.