How to Do Linear Inequalities
- 1). Solve a linear inequality using algebra to isolate the variable on one side of the inequality symbol. Change the direction of the inequality symbol if a negative number is multiplied or divided across the symbol during the solution.
- 2). Practice by solving the linear inequality -7x + 3 < 6 + 3x. Start isolating like terms by subtracting 3 from both sides: -7x < 3 + 3x. Subtract 3x from both sides: -10x < 3. Divide both sides by -10: x < - 3/10. Change the direction of the inequality symbol since you divided by a negative number: x > -3/10 or x > -0.3.
- 3). Check your answer by plugging x = -0.3 back into the original inequality: -7 * -0.3 + 3 < 6 + 3 * -0.3 or -2.1 + 3 < 6 + -0.9 or 0.9 < 5.1, which proves true.
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