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11. If [tex][tex]$4(x-3)=3(x-2)-5$[/tex][/tex], then [tex]$x=$[/tex]

A. [tex]$-\frac{1}{7}$[/tex]
B. [tex][tex]$-\frac{23}{7}$[/tex][/tex]
C. 1
D. [tex]$\frac{1}{7}$[/tex]
E. -1

Sagot :

GinnyAnsweridn
Certainly! Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex].

Given the equation:
[tex]\[ 4(x - 3) = 3(x - 2) - 5 \][/tex]

First, we need to distribute the constants inside the parentheses:

[tex]\[ 4(x - 3) = 4x - 12 \][/tex]
[tex]\[ 3(x - 2) - 5 = 3x - 6 - 5 \][/tex]

Simplify the right-hand side of the equation:
[tex]\[ 3x - 6 - 5 = 3x - 11 \][/tex]

Now our equation is transformed to:
[tex]\[ 4x - 12 = 3x - 11 \][/tex]

Next, we need to get all terms involving [tex]\( x \)[/tex] on one side of the equation and the constant terms on the other side. Subtract [tex]\( 3x \)[/tex] from both sides:

[tex]\[ 4x - 3x - 12 = -11 \][/tex]
[tex]\[ x - 12 = -11 \][/tex]

Then, add 12 to both sides to isolate [tex]\( x \)[/tex]:

[tex]\[ x - 12 + 12 = -11 + 12 \][/tex]
[tex]\[ x = 1 \][/tex]

So, the value of [tex]\( x \)[/tex] is:

[tex]\[ x = 1 \][/tex]

Therefore, the correct answer is:

C. 1
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