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What is the value of [tex]$x$[/tex] in the equation [tex]$3x - 4y = 65$[/tex], when [tex][tex]$y = 4$[/tex][/tex]?

A. [tex]x = 13 \frac{1}{4}[/tex]
B. [tex]x = 21 \frac{2}{3}[/tex]
C. [tex]x = 23[/tex]
D. [tex]x = 27[/tex]


Sagot :

To solve the equation [tex]\( 3x - 4y = 65 \)[/tex] for [tex]\( x \)[/tex] when [tex]\( y = 4 \)[/tex], follow these steps:

1. Substitute [tex]\( y = 4 \)[/tex] into the equation:
[tex]\[ 3x - 4(4) = 65 \][/tex]

2. Simplify the equation:
[tex]\[ 3x - 16 = 65 \][/tex]

3. Add 16 to both sides to isolate [tex]\( 3x \)[/tex]:
[tex]\[ 3x - 16 + 16 = 65 + 16 \][/tex]
[tex]\[ 3x = 81 \][/tex]

4. Divide both sides of the equation by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{3x}{3} = \frac{81}{3} \][/tex]
[tex]\[ x = 27 \][/tex]

Thus, the value of [tex]\( x \)[/tex] when [tex]\( y = 4 \)[/tex] is [tex]\( x = 27 \)[/tex].

So, the correct answer is [tex]\( \boxed{x = 27} \)[/tex].