solve 2x- 8 / 5x + 2 = 3/2
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Question :-
Solve -
[tex]\rm \dfrac{2x - 8}{5x + 2} = \dfrac{3}{2}[/tex]
Solution :-
[tex]\rm \dfrac{2x - 8}{5x + 2} = \dfrac{3}{2}[/tex]
By cross multiplication :-
➩ [tex]\rm 2(2x - 8) = 3(5x + 2)[/tex]
➩ [tex]\rm 4x - 16 = 15x + 6 [/tex]
➩ [tex]\rm 15x - 4x = - 16 - 6[/tex]
➩ [tex]\rm 11x = - 22 [/tex]
➩ [tex]\rm x = \dfrac{ - \cancel{ 22}}{\cancel {11}} [/tex]
➩ [tex]\boxed{\rm x = - 2}[/tex]
Verification :-
➩ [tex]\rm LHS = \dfrac{2x - 8}{5x + 2} [/tex]
➩ [tex]\rm \dfrac{2( - 2) - 8}{5( - 2) + 2} [/tex]
➩ [tex]\rm \dfrac{ - 4 - 8}{ - 10 + 2} [/tex]
➩ [tex]\rm \dfrac{ - 12}{ - 8} [/tex]
➩ [tex]\rm LHS = \frac{3}{2} = RHS[/tex]
Hence verified.
Step-by-step explanation:
Solve -
\rm \dfrac{2x - 8}{5x + 2} = \dfrac{3}{2}
5x+2
2x−8
=
2
3
Solution :-
\rm \dfrac{2x - 8}{5x + 2} = \dfrac{3}{2}
5x+2
2x−8
=
2
3
By cross multiplication :-
➩ \rm 2(2x - 8) = 3(5x + 2)2(2x−8)=3(5x+2)
➩ \rm 4x - 16 = 15x + 64x−16=15x+6
➩ \rm 15x - 4x = - 16 - 615x−4x=−16−6
➩ \rm 11x = - 2211x=−22
➩ \rm x = \dfrac{ - \cancel{ 22}}{\cancel {11}}x=
11
−
22
➩ \boxed{\rm x = - 2}
x=−2
Verification :-
➩ \rm LHS = \dfrac{2x - 8}{5x + 2}LHS=
5x+2
2x−8
➩ \rm \dfrac{2( - 2) - 8}{5( - 2) + 2}
5(−2)+2
2(−2)−8
➩ \rm \dfrac{ - 4 - 8}{ - 10 + 2}
−10+2
−4−8
➩ \rm \dfrac{ - 12}{ - 8}
−8
−12
➩ \rm LHS = \frac{3}{2} = RHSLHS=
2
3
=RHS
Hence verified.