Question

Which of the following equations have the same solution set? Give reasons for your answers that do not depend on solving the equations. l.x-5=3x+7 ll.3x-6=7x+8 lll.15x-9=6x+24 lV.6x-16=14x+12 V.9x+21=3x-15 Vl.-0.05+frac{x}{100}=3frac{x}{100}+0.07

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asked 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.\(x-5=3x+7\)
ll.\(3x-6=7x+8\)
lll.\(15x-9=6x+24\)
lV.\(6x-16=14x+12\)
V.\(9x+21=3x-15\)
Vl.\(-0.05+\frac{x}{100}=3\frac{x}{100}+0.07\)

Answers (1)

2020-10-28

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):
\((x-5)(3)=(3x+7)(3)\)
\(3x-15=9x+21\)
\(9x+21=3x-15\)
We can obtain Vl from l by multiplying both sides of l by 100 then applying commutative property on the left side:
\(\frac{x-5}{100}=\frac{3x+7}{100}\)
\(\frac{x}{100-0.05}=\frac{3x}{100+0.07}\)
\(\frac{-0.05+x}{100}=\frac{3x}{100}+0.07\)
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:
\((3x-6)(2)=(7x+8)(2)\)
\(6x-12=14x+16\)
\(6x-12-4=14x+16-4\)
\(6x-16=14x+12\)
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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