Solve - 2x-3-x-1-6-7x-1-4-21-6- Hence- find the value of -a- if 1-a-5x-8-

2x/3 x 1/6+7x 1/4=21/6 ⇒ 2x/3 x 1/6+7x 1/4=13/6 =8x 2x+2+21x 3=26/12 (L.C.M. of 3, 6, 4, 6 = 12) ⇒ 27x 1=26 ⇒ 27x=26+1 ⇒ x=27/27=1 Hence x=1 Now, 1/a+5x=8 ⇒ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Solving Equations with Linear Expressions on One Side and Numbers on the Other Side

Solve : 2x/3-...

Question

Solve : $\frac{2 x}{3} - \frac{x - 1}{6} + \frac{7 x - 1}{4} = 2 \frac{1}{6} .$

Hence, find the value of 'a', if $\frac{1}{a} + 5 x = 8.$

Open in App

Solution

$\frac{2 x}{3} - \frac{x - 1}{6} + \frac{7 x - 1}{4} = 2 \frac{1}{6} \Rightarrow \frac{2 x}{3} - \frac{x - 1}{6} + \frac{7 x - 1}{4} = \frac{13}{6} = \frac{8 x - 2 x + 2 + 21 x - 3 = 26}{12} (L.C.M. of 3, 6, 4, 6 = 12) \Rightarrow 27 x - 1 = 26 \Rightarrow 27 x = 26 + 1 \Rightarrow x = \frac{27}{27} = 1 Hence~x = 1 Now,~ \frac{1}{a} + 5 x = 8 \Rightarrow \frac{1}{a} + 5 \times 1 = 8 \Rightarrow \frac{1}{a} + 5 = 8 \Rightarrow \frac{1}{a} = 8 - 5 = 3 ∵ 3 a = 1 \Rightarrow a = \frac{1}{3} ∵ x = 1 and a = \frac{1}{3} .$

Suggest Corrections

Similar questions

\frac{2 x}{3} - \frac{x - 1}{6} + \frac{7 x - 1}{4} = 2 \frac{1}{6}

Hence, find the value of

x

and

a

, if

\frac{1}{a} + 5 x = 8.

Q. Solve problem:

\frac{2 x}{3} - \frac{x - 1}{6} + \frac{7 x - 1}{4} = 2 \frac{1}{6}

Q. Find the value of

x

\frac{1 - x}{6} + \frac{2 x}{3} - \frac{1 - \frac{3}{7 x}}{4} = 2 \frac{1}{6}

Q. Solve:

\frac{2 x + 1}{10} - \frac{3 - 2 x}{15} = \frac{x - 2}{6}

. Hence, find y, if

\frac{1}{x} + \frac{1}{y} + 1 = 0

Q. (i) If

A = [\begin{matrix} 1 & - 2 & 0 \\ 2 & 1 & 3 \\ 0 & - 2 & 1 \end{matrix}]

, find A⁻¹. Using A⁻¹, solve the system of linear equations
x − 2y = 10, 2x + y + 3z = 8, −2y + z = 7

(ii)

A = [\begin{matrix} 3 & - 4 & 2 \\ 2 & 3 & 5 \\ 1 & 0 & 1 \end{matrix}]

, find A⁻¹ and hence solve the following system of equations:
3x − 4y + 2z = −1, 2x + 3y + 5z = 7, x + z = 2

(iii)

A = [\begin{matrix} 1 & - 2 & 0 \\ 2 & 1 & 3 \\ 0 & - 2 & 1 \end{matrix}] and B = [\begin{matrix} 7 & 2 & - 6 \\ - 2 & 1 & - 3 \\ - 4 & 2 & 5 \end{matrix}]

, find AB. Hence, solve the system of equations:
x − 2y = 10, 2x + y + 3z = 8 and −2y + z = 7

Join BYJU'S Learning Program

Solve : 2x3−x−16+7x−14=216. Hence, find the value of 'a', if 1a+5x=8.

2x3−x−16+7x−14=216⇒ 2x3−x−16+7x−14=136=8x−2x+2+21x−3=2612 (L.C.M. of 3, 6, 4, 6 = 12)⇒ 27x−1=26⇒ 27x=26+1⇒ x=2727=1Hence~x=1Now,~1a+5x=8⇒ 1a+5×1=8⇒ 1a+5=8⇒ 1a=8−5=3∵ 3a=1⇒ a=13∵ x=1 and a=13.

Solve : $\frac{2 x}{3} - \frac{x - 1}{6} + \frac{7 x - 1}{4} = 2 \frac{1}{6} .$

Hence, find the value of 'a', if $\frac{1}{a} + 5 x = 8.$