To solve the equation [tex]\( 4x - 6 = 10x - 3 \)[/tex], follow these detailed steps:
1. Subtract [tex]\( 10x \)[/tex] from both sides to move all the terms involving [tex]\( x \)[/tex] to one side of the equation.
[tex]\[
4x - 6 - 10x = 10x - 3 - 10x
\][/tex]
Simplifying each side, you get:
[tex]\[
4x - 10x - 6 = -3
\][/tex]
2. Combine like terms on the left side.
[tex]\[
-6x - 6 = -3
\][/tex]
3. Add 6 to both sides to isolate the term involving [tex]\( x \)[/tex] on one side.
[tex]\[
-6x - 6 + 6 = -3 + 6
\][/tex]
Simplifying both sides, you get:
[tex]\[
-6x = 3
\][/tex]
4. Divide both sides by -6 to solve for [tex]\( x \)[/tex].
[tex]\[
x = \frac{3}{-6}
\][/tex]
5. Simplify the fraction.
[tex]\[
x = -0.5
\][/tex]
Therefore, the solution to the equation [tex]\( 4x - 6 = 10x - 3 \)[/tex] is [tex]\( x = -0.5 \)[/tex].
