A student is attempting to solve a multi-step equation. Sample mathematical work is shown below. Which statement best applies to
the sample mathematical work?
Given the equation , I must solve for m. I first subtract 8 from both sides, which gives me
−m/2
= -25/3. I then multiply both sides by –2, which gives me the final answer of m=50/3
A) The student incorrectly subtracted 8 from both sides.
B) The student incorrectly multiplied both sides by –2.
C) The final answer is not reduced or simplified.
D) The mathematical work shown is correct
Given the equation , I must solve for m. I first subtract 8 from both sides, which gives me
−m/2
= -25/3. I then multiply both sides by –2, which gives me the final answer of m=50/3
A) The student incorrectly subtracted 8 from both sides.
B) The student incorrectly multiplied both sides by –2.
C) The final answer is not reduced or simplified.
D) The mathematical work shown is correct
1 answer:
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Equations with absolute value:
Where k is a positive number; if k is a negative number, the equation is impossible (absolute value is always positive).
How to solve:
Then:
1. |x+7|=12
x+7=12 V -x-7=12
x=5 V -x=19
x=5 V x=-19
{-19, 5}
2. |2x+4|=8
2x+4=8 V -2x-4=8
2x=4 V -2x=12
x=2 V x=-6
3. 3|3k|=27
3×3k=27 V 3×(-3k)=27
9k=27 V -9k=27
k=3 V k=-3
{-3, 3}
4. 5|b+8|=30
5×(b+8)=30 V 5×(-b-8)=30
5b+40=30 V -5b-40=30
5b=-10 V -5b=70
b=-2 V b=-14
{-14, -2}
5. |m+9|=5
m+9=5 V -m-9=5
m+9=5 V m+9=-5
Where k is a positive number; if k is a negative number, the equation is impossible (absolute value is always positive).
How to solve:
Then:
1. |x+7|=12
x+7=12 V -x-7=12
x=5 V -x=19
x=5 V x=-19
{-19, 5}
2. |2x+4|=8
2x+4=8 V -2x-4=8
2x=4 V -2x=12
x=2 V x=-6
3. 3|3k|=27
3×3k=27 V 3×(-3k)=27
9k=27 V -9k=27
k=3 V k=-3
{-3, 3}
4. 5|b+8|=30
5×(b+8)=30 V 5×(-b-8)=30
5b+40=30 V -5b-40=30
5b=-10 V -5b=70
b=-2 V b=-14
{-14, -2}
5. |m+9|=5
m+9=5 V -m-9=5
m+9=5 V m+9=-5