Questions: Solve the compound inequality. 2x - 1 ≥ -11 and 4x - 6 < 2 Graph the solution on the number line.

Transcript text: Solve the compound inequality. \[ 2 x-1 \geq-11 \text { and } 4 x-6<2 \] Graph the solution on the number line.

Solution

Step 1: Solve the first inequality \(2x - 1 \geq -11\)

Add 1 to both sides: \[2x - 1 + 1 \geq -11 + 1\] \[2x \geq -10\]

Divide both sides by 2: \[x \geq -5\]

Step 2: Solve the second inequality \(4x - 6 < 2\)

Add 6 to both sides: \[4x - 6 + 6 < 2 + 6\] \[4x < 8\]

Divide both sides by 4: \[x < 2\]

Step 3: Combine the solutions

The solution to the compound inequality is: \[-5 \leq x < 2\]

The solution to the compound inequality is \(-5 \leq x < 2\).

Graphically, this is represented on the number line as a closed circle at -5 and an open circle at 2, with a line connecting them.

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