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Use the properties of inequality to find the solution to

5(2𝑘−3)≥−3(4−3𝑘)

1 answer

To solve the inequality \( 5(2k - 3) \geq -3(4 - 3k) \), we will first simplify both sides of the inequality.

  1. Distribute on both sides: \[ 5(2k) - 5(3) \geq -3(4) + 3(3k) \] This simplifies to: \[ 10k - 15 \geq -12 + 9k \]

  2. Next, we will move all the terms involving \( k \) to one side and the constant terms to the other side. We do this by subtracting \( 9k \) from both sides: \[ 10k - 9k - 15 \geq -12 \] This simplifies to: \[ k - 15 \geq -12 \]

  3. Now, add 15 to both sides of the inequality: \[ k - 15 + 15 \geq -12 + 15 \] This simplifies to: \[ k \geq 3 \]

The solution to the inequality \( 5(2k - 3) \geq -3(4 - 3k) \) is: \[ k \geq 3 \]