Question

Can someone solve this? also, show work please. We need to find out what x is.

-6x + 13 = -5(7 +6x)​

Answer 1

Answer:
`\huge{ \boxed{ \bold{ \tt{ x = - 2}}}}`

Explanation:

`\sf{ - 6x + 13 = - 5(7 + 6x) }`

Distribute -5 through the parentheses

`\longrightarrow{ \sf{ - 6x + 13 =  - 5 * 7  + ( - 5 )* 6x}}`

`\longrightarrow{ \sf{ - 6x  + 13 =  - 35 + ( - 30x)}}`

`\text{Remember} : \sf{( + ) * ( - ) = ( - )}`

`\longrightarrow{ \sf{ - 6x + 13 =  - 35 - 30x}}`

Move 30x to left hand side and change it's sign

`\longrightarrow{ \sf{ - 6x + 30x + 13 = - 35}}`

Move 13 to R.H.S ( Right Hand Side ) and change it's sign
`\longrightarrow{ \sf{ - 6x + 30x= - 35 - 13}}`

Combine like terms

`\longrightarrow{ \sf{24x = - 35 - 13}}`

The negative integers are always added but posses the negative ( - ) sign.
`\longrightarrow{ \sf{24x = - 48 }}`

Divide both sides by 24

`\longrightarrow{ \sf{ (24x)/(24) = ( - 48)/(24)}}`

Dividing a negative integer by a positive integers gives a negative integer.

`\longrightarrow{\sf{x = -2 }}`

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Verification:

L.H.S = -6x + 13

Plug the value of x and simplify

`\longrightarrow{ \sf{ - 6 * ( - 2) + 13}}`

Multiplying negative integers by a negative integer gives a positive integer.

`\longrightarrow{ \sf{ 12 + 13}}`

Add the numbers : 12 and 13

`\longrightarrow{ \sf{25}}`

R.H.S = -5 ( 7 + 6x )

plug the value of x and simplify

`\longrightarrow{ \sf{ - 5(7 + 6 * ( - 2)}})`

Multiplying a positive integer by any negative integer gives a negative integer.

`\longrightarrow{ \sf - 5(7 + ( - 12)}`

`\longrightarrow{\sf{-5(7 - 12)}}`

Subtract 12 from 7

`\longrightarrow{ \sf{ - 5 * ( - 5)}}`

`\longrightarrow{\sf{25}}`

L.H.S = R.H.S

The value of x is -2 .

Hope I helped!

Best regards!

~TheAnimeGirl