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Solve for the value of x in this equation: -10x+17x-2 = 5(x+4)

I need help ASAP
Needs to be step by step

User JoonT
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2 Answers

3 votes
ok here are the steps and the answer
Solve for the value of x in this equation: -10x+17x-2 = 5(x+4) I need help ASAP Needs-example-1
User James Flight
by
7.1k points
3 votes

Answer:


\huge{ \bold{ \boxed{ \tt{x = 11}}}}

Explanation:


\text{ - 10x + 17x - 2 = 5(x + 4)}

Subtract 10x from 17x

10x and 17x are like terms. So, the coefficients of like terms can be added or subtracted.


\dashrightarrow{ \sf{ 7x - 2 = 5(x + 4)}}

Distribute 5 through the parentheses


\dashrightarrow{ \sf{7x - 2 = 5 * x + 5 * 4}}


\dashrightarrow{ \sf{7x - 2 = 5x + 20}}

Move 5x to left hand side ( L.H.S ) and change it's sign

Similarly , move 2 to right hand side ( R.H.S ) and change it's sign


\dashrightarrow{ \sf{7x - 5x = 20 + 2}}

Subtract 5x from 7x


\dashrightarrow{ \sf{2x = 20 + 2}}

Add the numbers : 20 and 2


\dashrightarrow{ \sf{2x = 22}}

Divide both sides by 2


\dashrightarrow{ \sf{ (2x)/(2) = (22)/(2)}}


\dashrightarrow{ \boxed{ \sf{x = 11}}}

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Now, let's check whether the value of x is 11 or not.

Verification :

L.H.S = n
\sf{ - 10x + 17x - 2}

Plug the value of x and simplify


\longrightarrow{ \sf{ - 10 * 11 + 17 * 11 - 2}}


\longrightarrow{ \sf{ - 110 + 187 - 2}}


\longrightarrow{ \sf{77 - 2}}


\dashrightarrow{ \sf{75}}

R.H.S =
\sf{5(x + 4)}

plug the value of x and simplify


\longrightarrow{ \sf{5(11 + 4)}}


\longrightarrow{ \sf{5 * \: 15}}


\longrightarrow{ \sf{75}}

L.H.S = R.H.S

The value of x is 11 .

--------------------------------------------------------------

Rules for solving an equation :

  • If an equation contains fractions , multiply each term by the LCM of denominators.
  • Remove the brackets , if any.
  • Collect the terms with the variable to the left hand side and constant terms to the right side by changing their signs ' + ' into ' - ' and ' - ' into ' + '
  • Simplify and get the single term on each side.
  • Divide each side by the coefficient of variable and then get the value of variable.

Hope I helped!

Best regards :D

~
\text{TheAnimeGirl}

User GTBebbo
by
6.4k points
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