Question

3m+5/4m+2 = 3m+4/4m+7​

Answer 1

Answer:

$\boxed{m = - \frac{27}{19}}$

Step-by-step explanation:

$Solve \: for \: m \: over \: the \: real \: numbers: \\ = > \frac{3m + 5}{4m + 2} = \frac{3m + 4}{4m + 7} \\ \\ Cross \: multiply: \\ (3m + 5)(4m + 7) = (3m + 4)(4m + 2) \\ \\ Expand \: out \: terms \: of \: the \: left \: hand \: side: \\ = > 3m(4m + 7) + 5(4m + 7) = (3m + 4)(4m + 2) \\ = > (3m \times 4m) + (3m \times 7) + (5 \times 4m) + (5 \times 7) = (3m + 4)(4m + 2) \\ = > 12 {m}^{2} + 21m + 20m + 35 = (3m + 4)(4m + 2) \\ = > 12 {m}^{2} + 41m + 35 = (3m + 4)(4m + 2) \\ \\ Expand \: out \: terms \: of \: the \: right \: hand \: side: \\ =>12 {m}^{2} +41m+35 =3m(4m + 2) + 4(4m + 2) \\ = >12 {m}^{2} +41m+35 = (3m \times 4m) + (3m \times 2) + (4 \times 4m) + (4 \times 2) \\ = > 12 {m}^{2} +41m+35 =12 {m}^{2} + 6m + 16m + 8 \\ = > 12 {m}^{2} +41m+35 =12 {m}^{2} + 22m + 8 \\ \\ Subtract \: 12 {m}^{2} + 22m + 8 \: from \: both \: sides : \\ = > 19m+27=0 \\ \\ Subtract \: 27 \: from \: both \: sides: \\ = > 19m =-27 \\ \\ Divide \: both \: sides \: by \: 19: \\ = > m = - \frac{27}{19}$

Answer 2

CORRECT QUESTION:

If 3m + 5/4m + 2 = 3m + 4/4m + 7 find the value of m

ANSWER:

(3m + 5)/(4m + 2) = (3m + 4)/(4m + 7)

Cross multiply

→ (4m + 2)(3m + 4) = (3m + 5)(4m + 7)

→ 12m² + 16m + 6m + 8 = 12m² + 21m + 20m + 35

Cancelling the like terms & taking the like terms to RHS & taking constant terms to LHS

→ 22m - 41m = 35 - 8

→ - 19m = 27……… ( i )

→ m = - 27/19 ( Required answer )

Hence, m = -27/19

VERIFICATION:

Taking Eq ( i ) & substituting the value of x

→ - 19(- 27/19) = 27

→ -19(-27) = 27

→ 27 = 27

LHS = RHS

Hence , verified !