Question

linear equation in one variable solve and verify the result

Answer 1

see here is ur answer
4{2x-(3-4x)=15{3x-(8-x)}
8x-12+16x=45x-120+15x
8x+16x-45x-15x= -120+12
-36x= -108
x= -108÷ -36
x=3
prove
2×3-3+4×3÷3×3-8+3=15÷4
15÷4=15÷4

Answer 2

Solution :

$\mathsf{\frac{2x - (3 - 4x)}{3x - (8 - x)} = \frac{15}{4}} \\ \\ \mathsf{ \frac{2x - 3 + 4x}{3x - 8 + x} = \frac{15}{4} } \\ \\ \mathsf{ \frac{6x - 3}{4x - 8} = \frac{15}{4}} \\ \\ \bold{on \: cross \: multiplying..} \\ \\ \mathsf{4(6x - 3) = 15(4x - 8)} \\ \\ \mathsf{24x - 12 = 60x - 120} \\ \\ \mathsf{24x - 60x = - 120 + 12} \ \\ \\ \mathsf{ \cancel - 36x = \cancel - 108 }\\ \\ \mathsf{36x = 108} \\ \\ \mathsf{x = \frac{108}{36}} \\ \\ \boxed {\bold{x = 3}}$

Verification :

Putting the value of x in the given equation ;

$\mathsf{\frac{2x - (3 - 4x)}{3x - (8 - x)} = \frac{15}{4}} \\ \\ \mathsf{ \frac{2(3) - (3 - 4 \times 3)}{3(3) - (8 - 3)} = \frac{15}{4} } \\ \\ \mathsf{ \frac{6 - (3 - 12)}{9 - (8 - 3)} = \frac{15}{4} } \\ \\ \mathsf{ \frac{6 - 3 + 12}{9 - 8 + 3} = \frac{15}{4} } \\ \\ \mathsf{ \frac{18 - 3}{12 - 8} = \frac{15}{4} } \\ \\ \mathsf{ \frac{15}{4} = \frac{15}{4} } \\ \\ \bold{ \therefore LHS = RHS }$

Hence, the value of x is 3.