The value of x from the given equation is -8. Luca did mistake while multiplying 5 inside the terms of a bracket.
The given equation is 2-6x=5-5(x-1).
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation can be solved as follows:
Using distributive property multiply 5 to the terms in a bracket.
That is, 2-6x=5-5x+5
⇒ 2-6x=10-5x
Add 5x to both the sides of an equation
That is, 2-6x+5x=10-5x+5x
⇒ 2-x = 10
Subtract 2 to both the sides of an equation
That is, -x=8
Multiply -1 to to both the sides of an equation
So, x=-8
The value of x from the given equation is -8. Luca did mistake while multiplying 5 inside the terms of a bracket.
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From the second and third steps, we know that m∠TUV = m∠1 + m∠2. We also know that m∠XWV = m∠3 + m∠4. Since ∠TUV and ∠XMV both measure 90°, we can set their measures equal to each other:
m∠TUV = m∠XMV
or equivalently:
m∠1 + m∠2 = m∠3 + m∠4
Next, we can use the fact that ∠1 ≅ ∠3 to say that m∠1 = m∠3, while allows us to replace one with the other. Here, we'll replace m∠3 with m∠1:
m∠1 + m∠2 = m∠1 + m∠4
Subtracting m∠1 from either side:
m∠2 = m∠4, which implies that ∠2 ≅ ∠4, as we wanted to show.