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If [tex][tex]$2x - 8 = 6 - 7x$[/tex][/tex] then [tex]$x =$[/tex]

A. [tex]\frac{14}{9}[/tex]
B. [tex]\frac{2}{9}[/tex]
C. [tex]-\frac{2}{9}[/tex]
D. [tex]-\frac{14}{9}[/tex]
E. [tex]-\frac{14}{5}[/tex]


Sagot :

Sure! Let's solve the equation [tex]\(2x - 8 = 6 - 7x\)[/tex] step by step.

1. First, we want to combine like terms by getting all the terms involving [tex]\(x\)[/tex] on one side of the equation and constants on the other side. To do this, we can add [tex]\(7x\)[/tex] to both sides of the equation:

[tex]\[2x - 8 + 7x = 6 - 7x + 7x\][/tex]

2. Simplify the equation by combining like terms:

[tex]\[2x + 7x - 8 = 6\][/tex]

[tex]\[9x - 8 = 6\][/tex]

3. Next, we need to isolate the [tex]\(x\)[/tex] term. To do this, add 8 to both sides of the equation:

[tex]\[9x - 8 + 8 = 6 + 8\][/tex]

4. Simplify the equation:

[tex]\[9x = 14\][/tex]

5. To solve for [tex]\(x\)[/tex], divide both sides of the equation by 9:

[tex]\[x = \frac{14}{9}\][/tex]

Therefore, the solution to the equation [tex]\(2x - 8 = 6 - 7x\)[/tex] is [tex]\(x = \frac{14}{9}\)[/tex].

So the correct answer is:
[tex]\[ \boxed{\frac{14}{9}} \][/tex]