To solve the equation [tex]\(4x - 6 = 10x - 3\)[/tex], follow these steps:
1. Isolate the terms involving [tex]\(x\)[/tex] on one side of the equation:
Start by moving the [tex]\(x\)[/tex]-terms to one side. Subtract [tex]\(10x\)[/tex] from both sides of the equation:
[tex]\[
4x - 10x - 6 = -3.
\][/tex]
2. Combine like terms:
Simplify the equation by combining the [tex]\(x\)[/tex]-terms on the left side:
[tex]\[
-6x - 6 = -3.
\][/tex]
3. Isolate the [tex]\(x\)[/tex]-term:
To isolate [tex]\(x\)[/tex], add 6 to both sides of the equation to move the constant term to the right side:
[tex]\[
-6x = -3 + 6.
\][/tex]
Simplify the right side:
[tex]\[
-6x = 3.
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides of the equation by [tex]\(-6\)[/tex] to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{3}{-6}.
\][/tex]
5. Simplify the fraction:
Simplify the fraction on the right side:
[tex]\[
x = -\frac{1}{2}.
\][/tex]
Thus, the solution to the equation [tex]\(4x - 6 = 10x - 3\)[/tex] is:
[tex]\[
x = -0.5.
\][/tex]
