Answer :

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].