Question

Solve the following linear equations and verify the solution: c) 1/x+2 + 1/4= 1/2

Answer 1

$\tt⇒ \frac{1}{x + 2} + \frac{1}{4}$

$\tt⇒ \frac{1}{x + 2} + \frac{ \frac{1}{4} \times (x + 2) }{x + 2}$

$\tt⇒ \frac{1 + \frac{1}{4} \times( x + 2) }{x + 2}$

$\tt⇒ \frac{1 + \frac{x + 2}{4} }{x + 2}$

$\t⇒t \frac{ \frac{x}{4} + \frac{x}{3} }{x + 2}$

$\tt⇒( \frac{x}{4} + \frac{3}{2} ) \times \frac{1}{x + 2}$

$\tt⇒ \frac{x + 6}{4} \times \frac{1}{x + 2}$

$\tt⇒ \frac{1}{4} \times x + 6 \times \frac{1}{x + 2}$

$\tt ⇒\frac{1}{4} \times \frac{1}{x + 2} \times x + 6$

$\tt⇒ \frac{x + 6}{4x + 8} = \frac{1}{2}$

$\tt❐ x = 2$

CelestialCentrix

Answer 2

Answer:

⇒

x+2

1

+

4

1

\begin{gathered} \tt⇒ \frac{1}{x + 2} + \frac{ \frac{1}{4} \times (x + 2) }{x + 2} \\ \end{gathered}

⇒

x+2

1

+

x+2

4

1

×(x+2)

\begin{gathered} \tt⇒ \frac{1 + \frac{1}{4} \times( x + 2) }{x + 2} \\ \end{gathered}

⇒

x+2

1+

4

1

×(x+2)

\begin{gathered} \tt⇒ \frac{1 + \frac{x + 2}{4} }{x + 2} \\ \end{gathered}

⇒

x+2

1+

4

x+2

\begin{gathered} \t⇒t \frac{ \frac{x}{4} + \frac{x}{3} }{x + 2} \\ \end{gathered}

\t⇒t

x+2

4

x

+

3

x

\begin{gathered} \tt⇒( \frac{x}{4} + \frac{3}{2} ) \times \frac{1}{x + 2} \\ \end{gathered}

⇒(

4

x

+

2

3

)×

x+2

1

\begin{gathered} \tt⇒ \frac{x + 6}{4} \times \frac{1}{x + 2} \\ \end{gathered}

⇒

4

x+6

×

x+2

1

\begin{gathered} \tt⇒ \frac{1}{4} \times x + 6 \times \frac{1}{x + 2} \\ \end{gathered}

⇒

4

1

×x+6×

x+2

1

\begin{gathered} \tt ⇒\frac{1}{4} \times \frac{1}{x + 2} \times x + 6 \\ \end{gathered}

⇒

4

1

×

x+2

1

×x+6

\begin{gathered} \tt⇒ \frac{x + 6}{4x + 8} = \frac{1}{2} \\ \end{gathered}

⇒

4x+8

x+6

=

2

1

\tt❐ x = 2❐x=2