Question

Match each step to solve the inequality with the statement that justifies it 2/3x 3>-5/3x-11?

Answer 1

To solve the inequality 2/3x + 3 > -5/3x - 11, add 5/3x to both sides, subtract 3 from both sides, combine like terms, and divide by the coefficient of x, remembering to reverse the inequality if multiplying or dividing by a negative.

Step-by-step explanation:

To solve the inequality 2/3x + 3 > -5/3x - 11, follow these steps:

1. Add 5/3x to both sides of the inequality to get all the x terms on one side. Justification: Applying the addition property of inequality.
2. Subtract 3 from both sides of the inequality to get all the constant terms on the other side. Justification: Applying the subtraction property of inequality.
3. Combine like terms on both sides, if necessary. Justification: This simplifies the expression, making the inequality easier to solve.
4. Divide both sides by the coefficient of x to isolate x. Justification: Applying the division property of inequality.

Remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign.