Question

X=−2 x=−1 x=1 6(0.5x−1.5)+2x=−9−(x+6) x = − 2 – 6 ( 0.5 x − 1.5 ) + 2 x = − 9 − ( x + 6 ) x = − 1 – 6 ( 0.5 x − 1.5 ) + 2 x = − 9 − ( x + 6 ) x = 1 – 6 ( 0.5 x − 1.5 ) + 2 x = − 9 − ( x + 6 ) 4(0.5x−2)+3x=−14−(x+6) x = − 2 – 4 ( 0.5 x − 2 ) + 3 x = − 14 − ( x + 6 ) x = − 1 – 4 ( 0.5 x − 2 ) + 3 x = − 14 − ( x + 6 ) x = 1 – 4 ( 0.5 x − 2 ) + 3 x = − 14 − ( x + 6 ) 8(0.5x−3)+4x=−9−(x+6)

Answer 1

Given:

Three equations are

`6(0.5x-1.5)+2x=-9-(x+6)`

`4(0.5x-2)+3x=-14-(x+6)`

`8(0.5x-3)+4x=-9-(x+6)`

Three solutions are
`x=-2,x=-1,x=1`.

To find:

The solution of each equation from the given solutions.

Solution:

We have,

`6(0.5x-1.5)+2x=-9-(x+6)`

Using distributive property, we get

`3x-9+2x=-9-x-6`

`5x-9=-15-x`

Isolate variable terms.

`5x+x=-15+9`

`6x=-6`

Divide both sides by 6.

`x=-1`

Similarly,

`4(0.5x-2)+3x=-14-(x+6)`

`2x-8+3x=-14-x-6`

`5x-8=-20-x`

`5x+x=-20+8`

`6x=-12`

`x=-2`

Now,

`8(0.5x-3)+4x=-9-(x+6)`

`4x-24+4x=-9-x-6`

`8x-24=-15-x`

`8x+x=-15+24`

`9x=9`

`x=1`

Therefore, the solutions of given equations
`6(0.5x-1.5)+2x=-9-(x+6)`,
`4(0.5x-2)+3x=-14-(x+6)` and
`8(0.5x-3)+4x=-9-(x+6)` are x=-1, x=-2 and x=1 respectively.