Question

Solve for z : 2(5z – 7) = 4(2z – 3) – 8​

Answer 1

$\large\underline{\sf{Solution-}}$

Given equation is

$\rm \: 2(5z - 7) = 4(2z - 3) - 8$

can be rewritten as

$\rm \: 10z - 14 = 8z - 12 - 8$

$\rm \: 10z - 14 = 8z - 20$

On transposition, we get

$\rm \: 10z -8z = - 20 + 14$

$\rm \: 2z = - 6$

$\rm\implies \:z \: = \: - \: 3$

Verification

Consider LHS

$\rm \: 2(5z - 7)$

On substituting the value of z, we get

$\rm \: = \: 2(5 \times ( - 3) - 7)$

$\rm \: = \: 2( - 15 - 7)$

$\rm \: = \: 2 \times ( - 22)$

$\rm \: = \: - 44$

Now, Consider RHS

$\rm \: 4(2z - 3) - 8$

On substituting the value of z, we get

$\rm \: = \: 4(2 \times ( - 3) - 3) - 8$

$\rm \: = \: 4( - 6 - 3) - 8$

$\rm \: = \: 4( - 9) - 8$

$\rm \: = \: - 36 - 8$

$\rm \: = \: - 44$

$\rm\implies \:LHS = RHS$

Hence, Verified

Answer 2

⇢ 2(5z – 7) = 4(2z – 3) – 8

⇢ 10z - 14 = 8z - 12 - 8

⇢ 10z - 14 = 8z - 20

⇢ 10z - 8z = - 20 + 14

⇢ 2z = -6

⇢ z = -6÷2

⇢ z = -6/2

⇢ z = -3