\( 1 \leftarrow \quad \) Solve and write interval notation for the solution set. Then graph the solution set. \( -9 \leq x+2<9 \) Isolate \( x \) in the compound inequality. \( \square \leq x<\square \) (Simplify your answers. Use integers or fractions for any numbers in the expression.)
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The Deep Dive
To solve the compound inequality \(-9 \leq x + 2 < 9\), we need to isolate \(x\). Start with the left side: \(-9 \leq x + 2\) Subtract \(2\) from both sides: \(-11 \leq x\) Now, tackle the right side: \(x + 2 < 9\) Subtract \(2\) from both sides again: \(x < 7\) Putting it together, we have: \(-11 \leq x < 7\) In interval notation, this is expressed as \([-11, 7)\). To graph the solution set, draw a number line, shade the region between \(-11\) and \(7\). Use a closed dot at \(-11\) (indicating it is included in the solution) and an open dot at \(7\) (indicating it is not included). Happy graphing!