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Question 1 of 5
Incorrect
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.
To solve for m, it needs to be alone on one side.
Start by expanding the left side of the equation by using the Distributive Property.
7(m +2)+2(6-2m) |
= |
4m |
7m +7(2)+2(6)+2(-2m) |
= |
4m |
7m +14+12-4m |
= |
4m |
3m +26 |
= |
4m |
Next, move 3m to the other side by subtracting 3m from both sides of the equation.
3m +26 |
= |
4m |
3m +26 -3m |
= |
4m -3m |
26 |
= |
m |
3m-3m cancels out |
m |
= |
26 |
Check our work
To confirm our answer, substitute m=26 to the original equation.
7(m+2)+2(6-2m) |
= |
4m |
7(26+2)+2(6-2(26)) |
= |
4(26) |
Substitute m=26 |
7(28)+2(6-52) |
= |
104 |
196+2(-46) |
= |
104 |
196-92 |
= |
104 |
104 |
= |
104 |
Since the equation is true, the answer is correct.
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Question 2 of 5
Solve
2(y+3)+5(y+2)=4(9-4y)-3(16-3y)
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.
Get y alone to the left side and all constants to the right.
Start by expanding both sides of the equation by using the Distributive Property.
2(y +3)+ 5(y +2) |
= |
4(9-4y)- 3(16-3y) |
2y+ 2(3)+ 5y+ 5(2) |
= |
4(9)- 4(4y)- 3(16)- 3(-3y) |
2y +6+5y+10 |
= |
36-16y -48+9y |
7y +16 |
= |
-7y -12 |
Next, move 16 to the other side by subtracting 16 from both sides of the equation.
7y +16 |
= |
-7y -12 |
7y +16 -16 |
= |
-7y -12 -16 |
7y |
= |
-7y -28 |
16-16 cancels out |
Then, move -7y to the other side by adding 7y to both sides of the equation.
7y |
= |
-7y -28 |
7y +7y |
= |
-7y -28 +7y |
14y |
= |
-28 |
-7y+7y cancels out |
Finally, remove 14 by dividing both sides of the equation by 14.
14y |
= |
-28 |
14y÷14 |
= |
-28÷14 |
y |
= |
-2 |
14÷14 cancels out |
Check our work
To confirm our answer, substitute y=-2 to the original equation.
2(y+3)+5(y+2) |
= |
4(9-4y)-3(16-3y) |
2(-2+3)+5(-2+2) |
= |
4(9-4(-2))-3(16-3(-2)) |
Substitute y=-2 |
2(1)+5(0) |
= |
4(9+8)-3(16+6) |
2+0 |
= |
4(17)-3(22) |
2 |
= |
68-66 |
2 |
= |
2 |
Since the equation is true, the answer is correct.
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Question 3 of 5
Solve for x
6(x+2)-4(x-1)=20
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To solve for x, get x by itself
Distribute the value inside the parenthesis.
6(x+2)-4(x-1) |
= |
20 |
|
|
|
6(x+2) |
= |
(x×6)+(2×6) |
|
= |
6x+12 |
|
|
|
-4(x-1) |
= |
(x×(-4))+(-1×(-4)) |
|
= |
-4x+4 |
|
|
|
(6x+12)+(-4x+4) |
= |
20 |
2x+16 |
= |
20 |
Subtract 16 from both sides of the equation
2x+16 -16 |
= |
20 -16 |
2x+16 -16 |
= |
20 -16 |
16-16 cancels out |
2x |
= |
4 |
2x÷2 |
= |
4÷2 |
Divide both sides by 2 |
2x÷2 |
= |
4÷2 |
×2÷2 cancels out |
x |
= |
2 |
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Question 4 of 5
Solve for v
-8v+7(v+8)=32-7v
Incorrect
To solve for v, get v by itself
Distribute the value inside the parenthesis.
-8v+7(v+8) |
= |
32-7v |
-8v+((v×7)+(8×7)) |
= |
32-7v |
-8v+7v+56 |
= |
32-7v |
-v+56 |
= |
32-7v |
Get the v variable on one side of the equation
-v+56 +7v |
= |
32-7v +7v |
Add 7v to both sides |
-v+56 +7v |
= |
32-7v +7v |
-7v+7v cancels out |
6v+56 |
= |
32 |
6v+56 -56 |
= |
32 -56 |
Subtract 56 from both sides |
6v+56 -56 |
= |
32 -56 |
56-56 cancels out |
6v |
= |
-24 |
6v÷6 |
= |
-24÷6 |
Divide both sides by 6 |
6v÷6 |
= |
-24÷6 |
×6÷6 cancels out |
v |
= |
-4 |
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Question 5 of 5
Solve for k
11-5k=4+7(1-5k)
Incorrect
To solve for k, get k by itself
Distribute the value inside the parenthesis.
11-5k |
= |
4+7(1-5k) |
11-5k |
= |
4+((1×7)+(-5k×7)) |
11-5k |
= |
4+7-35k |
11-5k |
= |
11-35k |
Get the k variable on one side of the equation
11-5k +5k |
= |
11-35k +5k |
Add 5k to both sides |
11-5k +5k |
= |
11-35k +5k |
-5k+5k cancels out |
11 |
= |
11-30k |
11 -11 |
= |
11-30k -11 |
Subtract 11 from both sides |
11 -11 |
= |
11-30k -11 |
11-11 cancels out on both sides |
0 |
= |
-30k |
0÷(-30) |
= |
30k÷(-30) |
Divide both sides by -30 |
0÷(-30) |
= |
30k÷(-30) |
×(-30)÷(-30) cancels out |
0 |
= |
k |
k |
= |
0 |