To solve the compound inequality \(-3 \leq 2x - 5 < 1\), we will tackle it in two parts.
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Solve the left part: \(-3 \leq 2x - 5\)
Add 5 to both sides: \[ 2 \leq 2x \]
Divide by 2: \[ 1 \leq x \quad \text{or} \quad x \geq 1 \]
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Solve the right part: \(2x - 5 < 1\)
Add 5 to both sides: \[ 2x < 6 \]
Divide by 2: \[ x < 3 \]
Now we combine these two results:
\[ 1 \leq x < 3 \]
In set notation, this is expressed as:
\[ {x: 1 \leq x < 3} \]
So the correct response is:
\({x:1 \leq x < 3}\)