**Linear Equations in One Variable **

## Exercise: 2.1

Solve the following equations and check your results.

1). 3*x *= 2*x *+ 18

3*x* – 2*x* = 18 transposing 2*x* to LHS

*x* = 18

2). 5*t *– 3 = 3*t *– 5

5*t *– 3*t* = – 5 + 3

2*t* = – 2

*t* = ^{–2}/_{2}

*t* = – 1

3). 5*x *+ 9 = 5 + 3*x *

5*x *– 3x = 5 – 9

2*x* = – 4

*x* = ^{–4}/_{2}

*x* = – 2

4). 4*z *+ 3 = 6 + 2*z *

4*z *– 2*z* = 6 – 3

2*z* = 3

*z* = ^{3}/_{2}

5). 2*x *– 1 = 14 – *x*

2*x *+ *x* = 14 + 1

3*x* = 15

*x* = ^{15}/_{3}

*x* = 5 * *

* *6). 8*x *+ 4 = 3 (*x *– 1) + 7

8*x *+ 4 = 3*x *– 3 + 7

8*x *+ 4 = 3*x *+ 4

8*x* – 3*x* = 4 – 4

5*x* = 0

*x* = ^{0}/_{5}

*x* = 0

7). *x *= ^{4}/_{5} (*x *+ 10)

5*x* =4(*x* + 10)

5*x* = 4*x* + 40

5*x* – 4*x* = 40

*x* = 40

8). ^{2}* ^{x}*/

_{3}+ 1 =

^{7}

*/*

^{x}_{15}+ 3

^{2}* ^{x}*/

_{3}–

^{7}

*/*

^{x}_{15}= 3 – 1 LCM of 3 and 5 is 15

^{10}* ^{x}*/

_{15}–

^{7}

*/*

^{x}_{15}= 2

^{10}^{x}^{-7x}/_{15} = 2

^{3}* ^{x}*/

_{15}= 2

* ^{x}*/

_{5}= 2

*x* = 2 X 5

*x* = 10

9). 2*y *+ ^{5}/_{3} = ^{26}/_{3} – *y*

2*y *+ *y* = ^{26}/_{3 }– ^{5}/_{3}

3*y* = ^{(26} – ^{5)}/_{3}

3*y* = ^{21}/_{3}

3*y* = 7

*y* = ^{7}/_{3}

10). 3*m *= 5*m *– ^{8}/_{5}

3*m *– 5*m *= ^{– 8}/_{5}

2m = ^{-8}/_{5}

m = ^{-8}/_{5} X ½

m = ^{4}/_{5}

Click here for the solutions of Std 8 Maths

1). Rational Numbers

2). Linear Equations in One Variable

3). Understanding Quadrilaterals

4). Data Handling