Question

I need help on question number 1 I have been stuck on it for a long time

Answer 1

Step-by-step explanation

Step 1

Vertical angles are formed when two lines intersect each other. Out of the 4 angles that are formed, the angles that are opposite to each other are vertical angles. vertical angles are congruent so

`\begin{gathered} m\angle5=m\angle7\rightarrow reason\text{ vertical angles} \\ \end{gathered}`

Step 1

replace the given values

`\begin{gathered} m\angle5=m\angle7\rightarrow reason\text{ vertical angles} \\ -2(3x-4)=3(x-3)-1 \end{gathered}`

now, we need to solve for x

a)

`\begin{gathered} -2(3x-4)=3(x-3)-1 \\ \text{apply distributive property} \\ -6x+8=3x-9-1 \\ \text{add like terms} \\ -6x+8=3x-10\rightarrow reason\text{ distributive property} \end{gathered}`

b)subtract 3x in both sides( additioin or subtraction property of equality)

`\begin{gathered} -6x+8=3x-10 \\ subtract\text{ 3x in both sides} \\ -6x+8-3x=3x-10-3x \\ -9x+8=-10 \\ \text{subtract 8 in both sides} \\ -9x+8-8=-10-8 \\ -9x=-18 \\ -9x=-18\rightarrow reason\colon\text{ addition and subtraction property of equality} \end{gathered}`

c) finally, divide both sides by (-9) division property of equality

`\begin{gathered} -9x=-18 \\ \text{divide both side by -9} \\ (-9x)/(-9)=(-18)/(-9) \\ x=2\rightarrow\text{prove} \end{gathered}`

i hope this helps you