emancipezN

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.$-0.05+\frac{x}{100}=3\frac{x}{100}+0.07$

Macsen Nixon

Expert

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):
$\left(x-5\right)\left(3\right)=\left(3x+7\right)\left(3\right)$
$3x-15=9x+21$
$9x+21=3x-15$
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:
$\left(3x-6\right)\left(2\right)=\left(7x+8\right)\left(2\right)$
$6x-12=14x+16$
$6x-12-4=14x+16-4$
$6x-16=14x+12$
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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