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Solve and check the equation.

[tex]\[ 6x - 3 = 5x - 7 \][/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice:

A. The solution set is [tex]\(\boxed{\text{ }\)[/tex].

(Type an integer or a simplified fraction.)

B. The solution set is [tex]\(\{x \mid x \text{ is a real number}\}\)[/tex].

C. The solution set is [tex]\(\varnothing\)[/tex].

Sagot :

GinnyAnswer
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].
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