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Solve for g.

6+6g≥g–4>1+6g

Write your answer as a compound inequality with integers.

1 answer

To solve the compound inequality \( 6 + 6g \geq g - 4 > 1 + 6g \), we will break it into two parts:

  1. \( 6 + 6g \geq g - 4 \)
  2. \( g - 4 > 1 + 6g \)

Step 1: Solve \( 6 + 6g \geq g - 4 \)

  1. Subtract \( g \) from both sides: \[ 6 + 5g \geq -4 \]

  2. Subtract 6 from both sides: \[ 5g \geq -10 \]

  3. Divide by 5: \[ g \geq -2 \]

Step 2: Solve \( g - 4 > 1 + 6g \)

  1. Subtract \( g \) from both sides: \[ -4 > 1 + 5g \]

  2. Subtract 1 from both sides: \[ -5 > 5g \]

  3. Divide by 5 (remember: dividing by a positive number does not flip the inequality): \[ -1 > g \quad \text{or} \quad g < -1 \]

Step 3: Combine the results

From the two parts, we have:

  • \( g \geq -2 \)
  • \( g < -1 \)

Final Result:

The combined solution is: \[ -2 \leq g < -1 \]

Thus, the solution as a compound inequality with integers is: \( -2 \leq g < -1 \).