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Solve the inequality, 4-3(2-x) < 10+x.

Solve the inequality, 4-3(2-x)<10+x .

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Full solution

Q. Solve the inequality, 4−3(2−x)<10+x 4-3(2-x)<10+x .
  1. Distribute −3-3: Distribute −3-3 across the terms inside the parentheses: 4−3(2−x)=4−6+3x4 - 3(2-x) = 4 - 6 + 3x.
  2. Combine like terms: Combine like terms on the left side of the inequality: 4−6+3x=−2+3x4 - 6 + 3x = -2 + 3x.
  3. Rewrite inequality: Rewrite the inequality with the simplified left side: -2 + 3x < 10 + x.
  4. Subtract xx: Subtract xx from both sides to get all xx terms on one side: -2 + 3x - x < 10 + x - x.
  5. Combine like terms: Combine like terms: -2 + 2x < 10.
  6. Add to isolate term: Add 22 to both sides to isolate the term with xx: -2 + 2 + 2x < 10 + 2.
  7. Combine like terms: Combine like terms: 2x < 12.
  8. Divide to solve: Divide both sides by 22 to solve for xx: \frac{2x}{2} < \frac{12}{2}.
  9. Simplify inequality: Simplify the inequality: x < 6.

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