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

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

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.