Question

please so this one
chapter= Simple Linear Equations.
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Answer 1

Required Solution:

$\sf{ \dfrac{z}{7} + 1 = 2 \dfrac{1}{2} }$

Here, we have to find the value of the variable z in the above equation.

Step 1 : Making mixed fraction in proper fraction in R.H.S.

$\implies \sf{ \dfrac{z}{7} + 1 = \dfrac{5}{2} }$

Step 2 : Taking the LCM in L.H.S and solving it.

$\implies \sf{ \dfrac{z + 7}{7} = \dfrac{5}{2} }$

Step 3 : Applying cross multiplication method.

$\implies \sf{ 2(z + 7) = 7(5)}$

Step 4 : Performing multiplication.

$\implies \sf{ 2z + 14 = 35}$

Step 5 : Transposing 14 from LHS to RHS.

$\implies \sf{ 2z = 35 - 14}$

Step 6 : Performing substraction in RHS.

$\implies \sf{ 2z = 21}$

Step 7 : Transposing 2 from LHS to RHS.

$\implies \sf{ z = \dfrac{21}{2} }$

Step 8 : Performing division.

$\implies \sf\red{ z = 10.5}$

Thus, value of z is 10.5.

Extra Information:

When we apply transposition method, signs are changed.

• If (+x) is transposed from L.H.S to R.H.S or vice versa, then its sign becomes (-x)

• If (-x) is transposed from L.H.S to R.H.S or vice versa, then its sign becomes (+x)

• If any number (x) is in multiplication form in L.H.S or R.H.S, its sign changed to division when it is transposed from L.H.S to R.H.S.

Let us understand with example :

• x + 2 = 4

→ x = 4 - 2

→ x = 2

Here, we transposed "+2" from L.H.S to R.H.S and hence its sign changed to "-2".

• y - 4 = 3

→ y = 3 + 4

→ y = 7

Here, we transposed "-4" from L.H.S to R.H.S and hence its sign changed to "+4".

• $\sf { \dfrac{a}{2}= 2}$

→ $\sf { a = 2 \times 2}$

→ $\sf {a = 4}$

Here, 2 is in division form in L.H.S. So, when we transposed it from L.H.S to R.H.S , its sign changed from division to multiplication.