To find the value of [tex]\( x \)[/tex] given the equations [tex]\( TV = 10x - 26 \)[/tex] and [tex]\( VX = 5x + 9 \)[/tex], we need to set the two expressions equal to each other and solve for [tex]\( x \)[/tex].
1. Start with the given equations:
[tex]\[
TV = 10x - 26
\][/tex]
[tex]\[
VX = 5x + 9
\][/tex]
2. Set [tex]\( TV \)[/tex] equal to [tex]\( VX \)[/tex]:
[tex]\[
10x - 26 = 5x + 9
\][/tex]
3. To eliminate [tex]\( 5x \)[/tex] from the right side, subtract [tex]\( 5x \)[/tex] from both sides:
[tex]\[
10x - 5x - 26 = 5x - 5x + 9
\][/tex]
Simplify the expressions:
[tex]\[
5x - 26 = 9
\][/tex]
4. To isolate [tex]\( 5x \)[/tex], add 26 to both sides:
[tex]\[
5x - 26 + 26 = 9 + 26
\][/tex]
Simplify the expressions:
[tex]\[
5x = 35
\][/tex]
5. Divide both sides by 5 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{35}{5}
\][/tex]
[tex]\[
x = 7
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 7 \)[/tex]. The correct answer is [tex]\( 7^\circ \)[/tex].
