Question

Find the solution for following equations:
(a) x +1=5
(b) 2x - 2 = 6
(c) 3x-2=7
(d) 4x – 4 = 12
(e) 5x-3=7​

Answer 1

Answer:

a) x = 4

b) x = 4

c) X = 3

d) x = 4

e) x = 2

Answer 2

Answer:

• (a), x = 4
• (b), x = 4
• (c), x = 3
• (d), x = 4
• (e), x = 2

Step-by-step explanation:

There are few equations given, They are :

• (a) x + 1 = 5
• (b) 2x – 2 = 6
• (c) 3x – 2 = 7
• (d) 4x – 4 = 12
• (e) 5x – 3 = 7

In order to calculate the value of x in each equation, We will use transposing method and solve it!

$\rule{200}2$

First equation!

(a) x + 1 = 5

Transposing 1 to RHS, Changing it's sign.

$\begin{gathered} \longmapsto \rm x = 5 - 1 \end{gathered}$

Performing subtraction.

$\begin{gathered} \longmapsto \rm x = 4\end{gathered}$

∴ The value of x in x + 1 = 5 is 4.

$\rule{200}2$

Second equation!

(b) 2x – 2 = 6

Transposing – 2 from LHS to RHS, Changing it's sign.

$\begin{gathered} \longmapsto \rm 2x = 6 + 2\end{gathered}$

Performing addition.

$\begin{gathered} \longmapsto \rm 2x = 8\end{gathered}$

Transposing 2 to the other side. Changing it's sign from (×) to (÷)

$\begin{gathered} \longmapsto \rm x = \dfrac{8}{2} \end{gathered}$

Performing division.

$\begin{gathered} \longmapsto \rm x = 4 \end{gathered}$

∴ The value of x in 2x - 2 = 6 is 4.

$\rule{200}2$

Third equation!

(c) 3x – 2 = 7

Transposing 2 to the other side.

$\begin{gathered} \longmapsto \rm 3x = 7 + 2 \end{gathered}$

Performing addition.

$\begin{gathered} \longmapsto \rm 3x = 9 \end{gathered}$

Transposing 3 to the other side. Changing it's sign from (×) to (÷)

$\begin{gathered} \longmapsto \rm x = \dfrac{9}{3} \end{gathered}$

Performing division.

$\begin{gathered} \longmapsto \rm x = 3 \end{gathered}$

∴ The value of x in 3x – 2 = 7 is 3.

$\rule{200}2$

Fourth equation!

(d) 4x – 4 = 12

Transposing 4 to the other side.

$\begin{gathered} \longmapsto \rm 4x = 12 + 4 \end{gathered}$

Performing addition in RHS.

$\begin{gathered} \longmapsto \rm 4x = 16 \end{gathered}$

Transposing 4 to the other side.

$\begin{gathered} \longmapsto \rm x = \dfrac{16}{4} \end{gathered}$

Performing division.

$\begin{gathered} \longmapsto \rm x = 4 \end{gathered}$

∴ The value of x in 4x – 4 = 12 is 4.

$\rule{200}2$

Fifth equation!

(e) 5x - 3 = 7

Transposing -3 to the other side.

$\begin{gathered} \longmapsto \rm 5x = 7 + 3\end{gathered}$

Performing addition in RHS.

$\begin{gathered} \longmapsto \rm 5x = 10\end{gathered}$

Transposing 5 to the other side.

$\begin{gathered} \longmapsto \rm x = \frac{10}{5} \end{gathered}$

Performing division.

$\begin{gathered} \longmapsto \rm x = 2\end{gathered}$

∴ The value of x in 5x - 3 = 7 is 2.