Respuesta :
Answer:
[tex]x = -57[/tex]
Step-by-step explanation:
-Solve for the value of x :
[tex]\frac{x}{9} - \frac{x+2}{3} = 12[/tex]
-Multiply both sides by [tex]9[/tex] and the least common multiple of [tex]9[/tex] is [tex]3[/tex] :
[tex]9\times \frac{x}{9} - \frac{x+2}{3} = 12 \times 9[/tex]
[tex]x - 3 (x + 2) = 108[/tex]
-Use Distributive Property :
[tex]x - 3 (x + 2) = 108[/tex]
[tex]x - 3x - 6 = 108[/tex]
-Combine both [tex]x[/tex] and [tex]-3x[/tex] :
[tex]x - 3x - 6 = 108[/tex]
[tex]-2x - 6 = 108[/tex]
-Add both sides by [tex]6[/tex] :
[tex]-2x - 6 + 6 = 108 + 6[/tex]
[tex]-2x = 114[/tex]
-Divide both sides by [tex]-2x[/tex] :
[tex]\frac{-2x}{-2} = \frac{114}{-2}[/tex]
[tex]x = -57[/tex]
So, the value of x is [tex]-57[/tex].
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 57}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ \frac{x}{9} - \frac{x + 2}{3} = 12}[/tex]
Take the L.C.M of 9 and 3
To do so, First of all find the prime factors of each numbers.
9 = 3 × 3 × 1
3 = 3 × 1
Take out the common prime factors i.e 3 and 1
Also take out the other remaining prime factor : 3
Multiply those all prime factors and obtain L.C.M
= 3 × 3 × 1 = 9
L.C.M of 9 and 3 = 9
[tex] \longrightarrow{ \sf{ \frac{x - 3(x + 2)}{9} = 12}}[/tex]
Distribute 3 through the parentheses
[tex] \longrightarrow{ \sf{ \frac{x - 3x - 6}{9} = 12}}[/tex]
Collect like terms
[tex] \longrightarrow{ \sf{ \frac{ - 2x - 6}{9} = 12}}[/tex]
Do cross multiplication
[tex] \longrightarrow{ \sf{ - 2x - 6 = 12 \times 9}}[/tex]
Multiply the numbers: 12 and 9
[tex] \longrightarrow{ \sf{ - 2x - 6 = 108}}[/tex]
Move 6 to right hand side and change it's sign
[tex] \longrightarrow{ \sf{ - 2x = 108 + 6}}[/tex]
Add the numbers: 108 and 6
[tex] \longrightarrow{ \sf{ - 2x = 114}}[/tex]
Divide both sides by -2
[tex] \longrightarrow{ \sf{ \frac{ - 2x}{ - 2} = \frac{114}{ - 2} }}[/tex]
Calculate
[tex] \longrightarrow{ \sf{x = - 57}}[/tex]
Hope I helped!
Best regards! :D
