Answer:[tex] \huge{ \boxed{ \bold{ \tt{ x = - 2}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ - 6x + 13 = - 5(7 + 6x) }[/tex]
Distribute -5 through the parentheses
[tex]\longrightarrow{ \sf{ - 6x + 13 = - 5 \times 7 + ( - 5 )\times 6x}}[/tex]
[tex]\longrightarrow{ \sf{ - 6x + 13 = - 35 + ( - 30x)}}[/tex]
[tex] \text{Remember} : \sf{( + ) \times ( - ) = ( - )}[/tex]
[tex]\longrightarrow{ \sf{ - 6x + 13 = - 35 - 30x}}[/tex]
Move 30x to left hand side and change it's sign
[tex] \longrightarrow{ \sf{ - 6x + 30x + 13 = - 35}}[/tex]
Move 13 to R.H.S ( Right Hand Side ) and change it's sign[tex] \longrightarrow{ \sf{ - 6x + 30x= - 35 - 13}}[/tex]
Combine like terms
[tex] \longrightarrow{ \sf{24x = - 35 - 13}}[/tex]
The negative integers are always added but posses the negative ( - ) sign.[tex] \longrightarrow{ \sf{24x = - 48 }}[/tex]
Divide both sides by 24
[tex] \longrightarrow{ \sf{ \frac{24x}{24} = \frac{ - 48}{24}}} [/tex]
Dividing a negative integer by a positive integers gives a negative integer.
[tex]\longrightarrow{\sf{x = -2 }}[/tex]
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Verification:
L.H.S = -6x + 13
Plug the value of x and simplify
[tex] \longrightarrow{ \sf{ - 6 \times ( - 2) + 13}}[/tex]
Multiplying negative integers by a negative integer gives a positive integer.
[tex] \longrightarrow{ \sf{ 12 + 13}}[/tex]
Add the numbers : 12 and 13
[tex] \longrightarrow{ \sf{25}}[/tex]
R.H.S = -5 ( 7 + 6x )
plug the value of x and simplify
[tex] \longrightarrow{ \sf{ - 5(7 + 6 \times ( - 2)}})[/tex]
Multiplying a positive integer by any negative integer gives a negative integer.
[tex] \longrightarrow{ \sf - 5(7 + ( - 12)}[/tex]
[tex]\longrightarrow{\sf{-5(7 - 12)}}[/tex]
Subtract 12 from 7
[tex] \longrightarrow{ \sf{ - 5 \times ( - 5)}}[/tex]
[tex]\longrightarrow{\sf{25}}[/tex]
L.H.S = R.H.S
The value of x is -2 .
Hope I helped!
Best regards!
~TheAnimeGirl
