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Question 1 of 4
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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.
6(2m +5) -5(3m +2) |
= |
26 |
6(2m)+6(5) -5(3m) -5(2) |
= |
26 |
12m +30-15m -10 |
= |
26 |
-3m +20 |
= |
26 |
Next, move 20 to the other side by subtracting 20 from both sides of the equation.
-3m +20 |
= |
26 |
-3m +20 -20 |
= |
26 -20 |
-3m |
= |
6 |
20-20 cancels out |
Finally, remove -3 by dividing both sides of the equation by -3.
-3m |
= |
6 |
-3m÷-3 |
= |
6÷-3 |
m |
= |
-2 |
-3÷-3 cancels out |
Check our work
To confirm our answer, substitute m=-2 to the original equation.
6(2m+5)-5(3m+2) |
= |
26 |
6(2(-2)+5)-5(3(-2)+2) |
= |
26 |
Substitute m=-2 |
6(-4+5)-5(-6+2) |
= |
26 |
6(1)-5(-4) |
= |
26 |
6+20 |
= |
26 |
26 |
= |
26 |
Since the equation is true, the answer is correct.
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Question 2 of 4
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.
To solve for y, it needs to be alone on one side.
Start by expanding the left side of the equation by using the Distributive Property.
8(2y +3)-4(3y +2) |
= |
32 |
8(2y)+8(3) -4(3y) -4(2) |
= |
32 |
16y +24-12y-8 |
= |
32 |
4y +16 |
= |
32 |
Next, move 16 to the other side by subtracting 16 from both sides of the equation.
4y +16 |
= |
32 |
4y +16 -16 |
= |
32 -16 |
4y |
= |
16 |
16-16 cancels out |
Finally, remove 4 by dividing both sides of the equation by 4.
4y |
= |
16 |
4y÷4 |
= |
16÷4 |
y |
= |
4 |
4÷4 cancels out |
Check our work
To confirm our answer, substitute y=4 to the original equation.
8(2y+3)-4(3y+2) |
= |
32 |
8[2(4)+3]-4[3(4)+2] |
= |
32 |
Substitute y=4 |
8(8+3)-4(12+2) |
= |
32 |
8(11)-4(14) |
= |
32 |
88-56 |
= |
32 |
32 |
= |
32 |
Since the equation is true, the answer is correct.
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Question 3 of 4
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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.
9(m +1) |
= |
3(m -3) |
9(m)+9(1) |
= |
3(m)+3(-3) |
9m +9 |
= |
3m -9 |
Next, move 9 to the other side by subtracting 9 from both sides of the equation.
9m +9 |
= |
3m -9 |
9m +9 -9 |
= |
3m -9 -9 |
9m |
= |
3m -18 |
9-9 cancels out |
Now, move 3m to the other side by subtracting 3m from both sides of the equation.
9m |
= |
3m -18 |
9m -3m |
= |
3m -18 -3m |
6m |
= |
-18 |
3m-3m cancels out |
Finally, remove 6 by dividing both sides of the equation by 6.
6m |
= |
-18 |
6m÷6 |
= |
-18÷6 |
m |
= |
-3 |
6÷6 cancels out |
Check our work
To confirm our answer, substitute m=-3 to the original equation.
9(m+1) |
= |
3(m-3) |
9(-3+1) |
= |
3(-3-3) |
Substitute m=-3 |
9(-2) |
= |
3(-6) |
-18 |
= |
-18 |
Since the equation is true, the answer is correct.
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Question 4 of 4
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.
To solve for a, it needs to be alone on one side.
Start by expanding the right side of the equation by using the Distributive Property.
2a +5 |
= |
6(a -4)-3a |
2a +5 |
= |
6a -6(4)-3a |
2a +5 |
= |
3a -24 |
Next, move 2a to the other side by subtracting 2a from both sides of the equation.
2a +5 |
= |
3a -24 |
2a +5 -2a |
= |
3a -24 -2a |
5 |
= |
a -24 |
2a-2a cancels out |
Now, move -24 to the other side by adding 24 to both sides of the equation.
5 |
= |
a -24 |
5 +24 |
= |
a -24 +24 |
29 |
= |
a |
-24+24 cancels out |
a |
= |
29 |
Check our work
To confirm our answer, substitute a=29 to the original equation.
2a+5 |
= |
6(a-4)-3a |
2(29)+5 |
= |
6(29-4)-3(29) |
Substitute a=29 |
58+5 |
= |
6(25)-87 |
63 |
= |
150-87 |
63 |
= |
63 |
Since the equation is true, the answer is correct.