What is the solution to the linear equation?
2/3x - 1/2=1/3 + 5/6x

The answer is x = -5

Step-by-step explanation:

2/3x - 1/2 = 1/3 + 5/6. First, multiply the entire equation by the common denominator of 6. This will get rid of the fractions. :)

6(2/3x - 1/2) = 6(1/3 + 5/6x)

4x - 3 = 2 + 5x subtract 5x from both sides

4x - 5x - 3 = 2 add 3 to both sides

4x - 5x = 2 + 3 combine terms

-x = 5 multiply by -1 to make x positive

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

1/6

step-by-step explanation: