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Complete the following questions and show all of your work.

What are the solutions to the compound inequality 6c+8≤−10
or 8c+12>20
?

simple equations no explanation

1 answer

To solve the compound inequality \( 6c + 8 \leq -10 \) or \( 8c + 12 > 20 \):

  1. Solve \( 6c + 8 \leq -10 \): \[ 6c + 8 \leq -10 \] Subtract 8 from both sides: \[ 6c \leq -10 - 8 \] \[ 6c \leq -18 \] Divide by 6: \[ c \leq -3 \]

  2. Solve \( 8c + 12 > 20 \): \[ 8c + 12 > 20 \] Subtract 12 from both sides: \[ 8c > 20 - 12 \] \[ 8c > 8 \] Divide by 8: \[ c > 1 \]

The solutions to the compound inequality \( 6c+8\leq−10 \) or \( 8c+12>20 \) are: \[ c \leq -3 \quad \text{or} \quad c > 1 \]