practice test 3\nperiod: a\nunit 2: lesson 2.6 - 2.11 algebra i assessment\nsection b: manipulating…

practice test 3\nperiod: a\nunit 2: lesson 2.6 - 2.11 algebra i assessment\nsection b: manipulating equations and understanding their structure\nunit 2. lesson 6: equivalent equations\nquestion 1\njada has a coin jar containing n nickels and d dimes worth a total of $3.65. the equation\n0.05n + 0.1d = 3.65 is one way to represent this situation.\nwhich equation is equivalent to the equation 0.05n + 0.1d = 3.65?\na. 5n + d = 365\nb. 0.5n + d = 365\nc. 5n + 10d = 365\nd. 0.05d + 0.1n = 365\nsolution c\nquestion 2\n2. select all the equations that have the same solution as 2x - 5 = 15.\na. 2x = 10\nb. 2x = 20\nc. 2(x - 5) = 15\nd. 2x - 20 = 0\ne. 6x - 15 = 45\nf. 25 = 5 - 2x\nsolution b, d, e

practice test 3\nperiod: a\nunit 2: lesson 2.6 - 2.11 algebra i assessment\nsection b: manipulating equations and understanding their structure\nunit 2. lesson 6: equivalent equations\nquestion 1\njada has a coin jar containing n nickels and d dimes worth a total of $3.65. the equation\n0.05n + 0.1d = 3.65 is one way to represent this situation.\nwhich equation is equivalent to the equation 0.05n + 0.1d = 3.65?\na. 5n + d = 365\nb. 0.5n + d = 365\nc. 5n + 10d = 365\nd. 0.05d + 0.1n = 365\nsolution c\nquestion 2\n2. select all the equations that have the same solution as 2x - 5 = 15.\na. 2x = 10\nb. 2x = 20\nc. 2(x - 5) = 15\nd. 2x - 20 = 0\ne. 6x - 15 = 45\nf. 25 = 5 - 2x\nsolution b, d, e

Answer

Explanation:

Step1: Solve (2x - 5=15)

Add (5) to both sides of the equation (2x-5 = 15). $$2x-5 + 5=15 + 5$$ $$2x=20$$

Step2: Analyze option a

For the equation (2x = 10), divide both sides by (2): (x=\frac{10}{2}=5). Since (2x = 20) gives (x = 10), option a is incorrect.

Step3: Analyze option b

For the equation (2x=20), divide both sides by (2): (x=\frac{20}{2}=10). This is the same as the solution of (2x - 5=15).

Step4: Analyze option c

Expand (2(x - 5)=15) using the distributive property (a(b - c)=ab-ac). (2x-10 = 15), then add (10) to both sides: (2x=15 + 10=25), and (x=\frac{25}{2}=12.5). Option c is incorrect.

Step5: Analyze option d

For the equation (2x-20 = 0), add (20) to both sides: (2x=20), then (x = 10). This is the same as the solution of (2x - 5=15).

Step6: Analyze option e

For the equation (4x-20 = 20), add (20) to both sides: (4x=20 + 20=40), then divide by (4): (x = 10). This is the same as the solution of (2x - 5=15).

Step7: Analyze option f

For the equation (25=5 - 2x), subtract (5) from both sides: (25-5=-2x), (20=-2x), then (x=-10). Option f is incorrect.

Answer:

b. (2x = 20), d. (2x-20 = 0), e. (4x - 20=20)