Questions: Solve the compound inequality. 2x + 4 < -8 or 4x - 4 > -4 Graph the solution on the number line.

Transcript text: Solve the compound inequality. \[ 2 x+4<-8 \text { or } 4 x-4>-4 \] Graph the solution on the number line.

Solution

Solution Steps

Step 1: Solve the first inequality

Solve $2x + 4 < -8$: \[ 2x + 4 < -8 \] Subtract 4 from both sides: \[ 2x < -12 \] Divide by 2: \[ x < -6 \]

Step 2: Solve the second inequality

Solve $4x - 4 > -4$: \[ 4x - 4 > -4 \] Add 4 to both sides: \[ 4x > 0 \] Divide by 4: \[ x > 0 \]

Step 3: Combine the solutions

The solution to the compound inequality $2x + 4 < -8 \text{ or } 4x - 4 > -4$ is: \[ x < -6 \text{ or } x > 0 \]

Final Answer

The solution to the compound inequality is: \[ x < -6 \text{ or } x > 0 \]

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -1, "ymax": 1}, "commands": ["y = 0 for x < -6", "y = 0 for x > 0"], "latex_expressions": ["$x < -6$", "$x > 0$"]}

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