Which of the following equations have the same solution set? Give reasons for your answers...

emancipezN

emancipezN

Answered

2020-10-27

Which of the following equations have the same solution set? Give reasons for your answers that do not depend on solving the equations.
l.x5=3x+7
ll.3x6=7x+8
lll.15x9=6x+24
lV.6x16=14x+12
V.9x+21=3x15
Vl.0.05+x100=3x100+0.07

Answer & Explanation

Macsen Nixon

Macsen Nixon

Expert

2020-10-28Added 117 answers

Equations l,V and Vl all have the same solution set.
We can obtain V from l by multiplying both sides of l by 3 then applying symmetric property(switching sides):
(x5)(3)=(3x+7)(3)
3x15=9x+21
9x+21=3x15
We can obtain Vl from l by multiplying both sides of l by 100 then applying commutative property on the left side:
x5100=3x+7100
x1000.05=3x100+0.07
0.05+x100=3x100+0.07
Equations ll and lV have the same solution set.
We can obtain lV from ll by multiplying both sides of ll by 2 then substracting 4 from both sides:
(3x6)(2)=(7x+8)(2)
6x12=14x+16
6x124=14x+164
6x16=14x+12
Equations lll does not have the same solution set as the other equations since it cannot be transformed from l or ll.
Results:l,V, and Vl all have the same solution set.
ll and lV have the same solution set.
lll does not have the same solution set as the other equations.

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