Let's analyze the inequalities step by step to find any possible errors.
Starting with Line (1): \[ -5 \leq 2x + 7 < 9 \]
We can break this compound inequality into two parts.
Part 1:
\[ -5 \leq 2x + 7 \] Subtract 7 from both sides: \[ -5 - 7 \leq 2x \Rightarrow -12 \leq 2x \] Dividing both sides by 2: \[ -6 \leq x \quad \text{(or rewritten as } x \geq -6) \]
Part 2:
\[ 2x + 7 < 9 \] Subtract 7 from both sides: \[ 2x < 9 - 7 \Rightarrow 2x < 2 \] Dividing both sides by 2: \[ x < 1 \]
Now we can combine the results from both parts.
From Part 1, we have: \[ -6 \leq x \quad \text{(or } x \geq -6) \] From Part 2, we have: \[ x < 1 \]
Putting both parts together, we get: \[ -6 \leq x < 1 \]
This matches Line (3): \[ -6 \leq x < 1 \]
There are no errors in the statements or the final result: The number line has a filled-in circle at \(-6\) (indicating it is included) and an open circle at \(1\) (indicating it is not included). The shading from \(-6\) to \(1\) is correct.
In conclusion, none of the lines contain errors and thus all calculations appear to be correct.
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