Answer:
The value of x in the given equation is x=16
Step-by-step explanation:
Given equation is [tex]\frac{1}{3}(2x-5)-2=\frac{1}{2}(x-2)[/tex]
To solve the given equation :
[tex]\frac{1}{3}(2x-5)-2=\frac{1}{2}(x-2)[/tex]
[tex]\frac{(2x-5)-6}{3}=\frac{1}{2}(x-2)[/tex]
[tex]2[(2x-5)-6]=3(x-2)[/tex] Multiplication property of equality
[tex]4x-10-12=3x-6[/tex] Distributive property
[tex]4x-22=3x-6[/tex] Simplify - combine like terms
[tex]4x-22+22=3x-6+22[/tex]
[tex]4x=3x+16[/tex] Addition property of equality
[tex]4x-(3x+16)=3x+16-(3x+16)[/tex] Subtraction property of equality
[tex]4x-3x-16=3x+16-3x-16[/tex] Distributive property
[tex]4x-3x-16=0[/tex]
[tex]x-16=0[/tex] Simplify combine like terms
[tex]x-16+16=0+16[/tex] Addition property of equality
[tex]x=16[/tex] Subtraction property of equality
Therefore the value of x in the given equation is x=16
