What property of inequality justifies the steps shown in the following solution process? 4/3d≥−20 3/4(4/3)d≥−20(3/4) d≥−15
Multiplication Property of Inequality Multiplication Property of Inequality Addition Property of Inequality Addition Property of Inequality Division Property of Inequality Division Property of Inequality Subtraction Property of Inequality
The property of inequality used in the steps shown in the solution process is the Multiplication Property of Inequality.
The property of inequality that justifies the steps shown in the solution process is the Multiplication Property of Inequality. According to this property, if we multiply both sides of an inequality by the same positive number, the inequality sign remains unchanged. In this case, the inequality 4/3d ≥ -20 can be multiplied by 3/4 on both sides, resulting in the inequality 3/4(4/3)d ≥ -20(3/4).
The property of inequality that justifies the steps shown in the solution process is the Multiplication Property of Inequality.
Let's break down the steps one by one:
1. Starting inequality: 4/3d ≥ -20
2. Multiplication by 3/4 on both sides: 3/4(4/3)d ≥ -20(3/4)
The Multiplication Property of Inequality states that if you multiply or divide both sides of an inequality by a positive number, the inequality sign remains the same. In this case, we are multiplying both sides by 3/4, which is a positive number, so the inequality sign remains the same.
3. Simplifying the left side: (3/4)(4/3)d = d
By simplifying the left side, we obtain d, which is the same variable as in the starting inequality.
4. Multiplying the right side: -20(3/4) = -15
When multiplying -20 by 3/4, we get -15.
5. Final inequality: d ≥ -15
By substituting d = (3/4)(4/3)d into the starting inequality, we get the final inequality d ≥ -15.
Therefore, the Multiplication Property of Inequality justifies the steps in this solution process.