2. 1.7 Solve Question 5, 1.7.29 Part 1 of 2 \( \begin{array}{l}\text { Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number } \\ \text { line. }\end{array} \)
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The Deep Dive
When solving inequalities, it's essential to first isolate the variable. For example, if you have an inequality like \( x + 3 < 7 \), you'd subtract 3 from both sides to get \( x < 4 \). In interval notation, this would be expressed as \( (-\infty, 4) \). Remember to use open brackets for inequalities where the variable can't equal the boundary number! Visualizing inequalities on a number line can be super helpful! For the example \( x < 4 \), you would represent it with an open circle at 4 (indicating that 4 itself isn't included) and shade everything to the left. This way, it's immediately clear what the solution set encompasses. So grab a ruler and have fun illustrating those ranges!