To solve the equation [tex]\(6x - 3 = 5x - 7\)[/tex], we will follow a step-by-step procedure:
1. Isolate the variable [tex]\(x\)[/tex]:
Start by getting all the [tex]\(x\)[/tex]-terms on one side of the equation and the constant terms on the other side. Subtract [tex]\(5x\)[/tex] from both sides of the equation:
[tex]\[
6x - 3 - 5x = 5x - 7 - 5x
\][/tex]
Simplify:
[tex]\[
x - 3 = -7
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
Add 3 to both sides of the equation to isolate [tex]\(x\)[/tex]:
[tex]\[
x - 3 + 3 = -7 + 3
\][/tex]
Simplify:
[tex]\[
x = -4
\][/tex]
So, the solution to the equation [tex]\(6x - 3 = 5x - 7\)[/tex] is [tex]\(x = -4\)[/tex].
3. Check the solution:
To verify if [tex]\(x = -4\)[/tex] is indeed the solution, substitute [tex]\(x = -4\)[/tex] back into the original equation and check both sides:
Left side:
[tex]\[
6(-4) - 3 = -24 - 3 = -27
\][/tex]
Right side:
[tex]\[
5(-4) - 7 = -20 - 7 = -27
\][/tex]
Both sides of the equation are equal ([tex]\(-27 = -27\)[/tex]), confirming that our solution is correct.
Choose the correct option:
A. The solution set is [tex]\(\{-4\}\)[/tex].
The correct choice is A. The solution set is [tex]\(\{-4\}\)[/tex].
