What property of inequality justifies the steps shown in the following solution process?
43d≥−20
34(43)d≥−20(34)
d≥−15
Responses
Multiplication Property of Inequality
Addition Property of Inequality
Subtraction Property of Inequality
Division 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
Responses
Subtraction Property of Inequality
Division Property of Inequality
Multiplication Property of Inequality
Addition 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
Responses
Juana and Anish
Giselle and Anish
Anish, Juana, and Giselle
Giselle and Juana
Anish, Juana, and Giselle
The property of inequality that justifies the steps shown in the solution process is the Multiplication Property of Inequality.
The property of inequality that justifies the steps in the solution process is the multiplication property of inequality.
To simplify the inequality 43d ≥ -20, the solution process multiplies both sides of the inequality by 34. By applying the multiplication property of inequality, which states that if a > b and c > 0, then ac > bc, we can multiply both sides of the inequality by the same positive number (in this case, 34) without changing the direction of the inequality sign.
So, by multiplying both sides of the inequality 43d ≥ -20 by 34, we get 34(43)d ≥ -20(34). This step is justified by the multiplication property of inequality.
The subsequent step in the solution process simplifies the equation further by multiplying -20 and 34, resulting in -680. So, the equation becomes 34(43)d ≥ -680.
Finally, to solve for d, we divide both sides of the inequality by 34. The division property of inequality states that if a > b and c > 0, then a/c > b/c. By applying this property, we can divide both sides of the inequality by the same positive number (in this case, 34) without changing the direction of the inequality sign.
Thus, dividing both sides of the inequality 34(43)d ≥ -680 by 34 gives us d ≥ -20.
In summary, the multiplication property of inequality justifies the steps in the given solution process.