What property of inequality justifies the steps shown in the following solution process? 43d≥−20 34(43)d≥−20(34) d≥−15 (1 point) Responses Multiplication Property of Inequality Multiplication Property of Inequality Subtraction Property of Inequality Subtraction Property of Inequality Division Property of Inequality Division Property of Inequality Addition Property of Inequality
Multiplication Property of Inequality
What property of inequality can justify the math in Step 2? Step 1: −6(3w−7)>−66 −18w+42>−66 Step 2: −18w+42−42>−66−42 −18w>−108 Step 3: −18w−18>−108−18 w<6 (1 point) Responses Subtraction Property of Inequality Subtraction Property of Inequality Addition Property of Inequality Addition Property of Inequality Multiplication Property of Inequality Multiplication Property of Inequality Division Property of Inequality
Subtraction Property of Inequality
Juana, Anish, and Giselle are comparing their solutions to the inequality 56x≤−10 . Juana says that the inequality symbol must be reversed because there is a negative sign in the inequality. Anish says the Multiplication Property of Inequality or Division Property of Inequality must be applied. Giselle says the inequality symbol must stay the same. Based on these answers, which combination of people is correct? (1 point) Responses Giselle and Juana Giselle and Juana Juana and Anish Juana and Anish Anish, Juana, and Giselle Anish, Juana, and Giselle Giselle and Anish Giselle and Anish
The correct combination of people is Anish, Juana, and Giselle.
Use the image to answer the question. What inequality does the number line graph? (1 point) Responses x<−7 x less than negative 7 x>−7 x greater than negative 7 x≤−7 x less-than-or-equal-to negative 7 x≥−7 x greater-than-or-equal-to negative 7
Based on the number line graph, the inequality being represented is x≥−7.
Graph x>11 .(1 point) Responses Image with alt text: A number line ranges from 5 to 15 in increments of 1. An open point is plotted at 11. An arrow extends indefinitely left from the open point past 5 along the number line. Image with alt text: A number line ranges from 5 to 15 in increments of 1. A closed point is plotted at 11. An arrow extends indefinitely left from the closed point past 5 along the number line. Image with alt text: A number line ranges from 5 to 15 in increments of 1. A closed point is plotted at 11. An arrow extends indefinitely right from the closed point past 15 along the number line.
The correct response is: An arrow extends indefinitely right from the closed point at 11, as shown in the third image description option.
The property of inequality that justifies the steps shown in the given solution process is the Multiplication Property of Inequality.
The Multiplication Property of Inequality states that if you multiply or divide both sides of an inequality by a positive number, the direction of the inequality sign remains the same. In other words, if you multiply or divide both sides of an inequality by a positive number, the inequality remains true.
In this case, the steps in the solution process involve multiplying both sides of the inequality by the number 34. According to the Multiplication Property of Inequality, when multiplying by a positive number (34 in this case), the direction of the inequality sign does not change. Hence, it is valid to multiply both sides of the inequality by 34.
Therefore, the correct answer is the Multiplication Property of Inequality.