- The first inequality, 3x + 7 > 19, is solved correctly. Subtracting 7 from both sides gives 3x > 12, and dividing by 3 gives x > 4. The graph correctly shows an open circle at 4 and shading to the right.
- The second inequality, 6 * (-2/3 x + 5/6) ≤ 1/3 * 6, is solved incorrectly. The multiplication on the left side should be -4x + 5, which is correct. However, when subtracting 5 from both sides, the result is -4x ≤ -3. Dividing by -4 requires flipping the inequality sign, so the correct solution is x ≥ 3/4. The final answer shown, x ≥ 3/4, is correct, but the step where the inequality sign is flipped is not indicated. The graph correctly shows a closed circle at 3/4 and shading to the right.
- The third inequality, -4(x - 3) < 12, is not solved. Dividing both sides by -4 requires flipping the inequality sign, giving x - 3 > -3. Adding 3 to both sides gives x > 0. The graph should show an open circle at 0 and shading to the right.
Parent Tip: Review the logic above to help your child master the concept of solving multi step inequalities worksheet.
