Algebra 2.11: Reasoning + quiz answers
The table shows the steps for solving the given inequality for x. −3(4−6x)<x+5 Select the reason for each step from the drop-down menus.
-3(4−6x)<x+5 Given −12+18x<x+5− Distributive Property −12+17x<5 Subtraction Property and Combine Like Terms 17x<17 Addition Property and Combine Like Terms x<1 Division Property of Inequality
Darius solved a two-step equation justifying both steps as shown. 1/4y+3=9 Determine if each justification is correct or incorrect.
1/4y=6: Addition Property of Equality incorrect y = 24: Multiplication Property of Equality correct
Drag the correct justification to each box. 2(y−5)+4=4 2y−10+4=4 [] 2y−6=4 [] 2y=10 [] y=5 []
2(y−5)+4=4 Given 2y−10+4=4 Distributive Property 2y−6=4 Addition 2y=10 Addition Property of Equality y=5 Division Property of Equality
Each step has been justified with a property to solve the inequality. 2.5y+2.5<2.5 Select true or false for each justification.
2.5y<0: Subtraction Property of Order True y<0: Division Property of Order True
Each step has been justified with a property to solve the equation. 21x−276=165 Select true or false for each justification.
21x=441: Addition Property of Equality True x=21: Multiplication Property of Equality False
Drag and drop the correct justification to each box. 25<2(4p)+1 25<8p+1 [] 24<8p [] 3<p [] p>3 []
25<2(4p)+1 25<8p+1 Multiplication 24<8p Subtraction Property of Order 3<p Division Property of Order p>3 Comparison Property of Order
Which property justifies each step in the transformation of the formula of the area of a trapezoid? A=1/2h(b1+b2) Drag and drop the answer into the box to match each step.
2A=h(b1+b2) Multiplication Property of Equality 2Ah=b1+b2 Division Property of Equality 2Ah−b2=b1 Subtraction Property of Equality
Kathy solved the inequality as shown. 2/5b≤20 Determine whether each justification is correct for each step.
2b≤100: Multiplication Property of Order correct b≤50: Division Property of Order correct
Reina solved the inequality as shown. 3/5d≥30 Determine whether each justification is correct for each step.
3d≥150: Multiplication Property of Inequality correct d≥50: Division Property of Inequality correct
Each step of solving the inequality is shown. 3x+3/6≤2 Drag and drop each justification to match the step.
3x+3≤12 Multiplication Property of Inequality 3x≤9 Subtraction Property of Inequality x≤3 Division Property of Inequality
Vasco solved 3x/4+1=10 as shown. Select the correct justification from the drop-down menu.
3x/4+1=10 Given 3x+4=40 Multiplication Property of Multiplication Property of Equality - correct 3x=36 Subtraction Property of Equality x=12 Division Property of Equality
What is the reason for each step in the solution of the equation? 3x−2=4 Drag and drop the reasons into the boxes to correctly complete the table.
3x−2=4 Given 3x=6 Addition Property of Equality x=2 Division Property of Equality
What line contains the incorrect justification when solving the inequality 5(x−3)+3x−1>20?
5x−15+3x−1>20 Multiplication Property of Order
Jamal solved this equation. 2+4x=2(2x+1) 2+4x=2⋅2x+2⋅1 2+4x=4x+2 2+4x−4x=4x−4x+2 2=2 Which statements are true? Select each correct answer.
The equation is an identity, There are infinitely many solutions. The equation is true for all values of x.
Is it also possible to solve 3x/4+1=10 by starting with the multiplication property of equality?
Yes
Each step of solving the inequality is shown. x/4+2.5≥7.5 Drag and drop each justification to match the step.
x/4≥5 Subtraction Property of Inequality x≥20 Multiplication Property of Inequality
What is the reason for each step in the solution of the inequality? 4(x+6)>−5(x+5)−14 Select the reason for each step from the drop-down menus.
4(x+6)>−5(x+5)−14 Given 4x+24>−5x−25−14 Distributive Property 4x+24>−5x−39 Combine Like Terms Only 4x+63>−5x Addition Property and Combine Like Terms 63>−9x Subtraction Property and Combine Like Terms −7<x− Division Property of Inequality
Each step of solving is shown. Justify each step with the correct property. 1/2−2y=1.5 Drag and drop the answer into the box to match each step.
−2y=1 Subtraction Property of Equality y=−12 Division Property of Equality
What is the reason for each step in the solution of the equation? −6x+7x+14=3 Drag and drop the reasons into the boxes to correctly complete the table.
−6x+7x+14=3 Given x+14=3 Combine Like Terms x=−11 Subtraction Property of Equality
What is the reason for each step in the solution of the equation? −6x=−2(x+12) Drag and drop the reasons into the boxes to correctly complete the table.
−6x=−2(x+12) Given −6x=−2x−24 Distributive Property −4x=−24 Addition Property of Equality x=6 Division Property of Equality
