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Georgia [21]
3 years ago
11

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

Mathematics
2 answers:
Basile [38]3 years ago
4 0

Answer:

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

Step-by-step 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 \times x  + 5 \times 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{ \frac{2x}{2}  =  \frac{22}{2}}}

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

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

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

<h3>Verification :</h3>

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

Plug the value of x and simplify

\longrightarrow{ \sf{ - 10 \times 11 + 17 \times 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 \times \: 15}}

\longrightarrow{ \sf{75}}

L.H.S = R.H.S

The value of x is 11 .

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

<h3>Rules for solving an equation :</h3>
  • 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}

zepelin [54]3 years ago
3 0
Ok here are the steps and the answer

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2 years ago
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Answer:

Equation of the line that passes through the given point and is (a) parallel is: \mathbf{y=-2x+11}

Equation of the line that passes through the given point and is (b) perpendicular is: \mathbf{y=\frac{1}{2}x+1}

Step-by-step explanation:

We need to Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.

First we will find slope of the line given in graph

The slope can be found using formula: Slope=\frac{y_2-y_1}{x_2-x_1}

We have points (1,6) and (2,2)

Slope is:

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Part a)

Write an equation of the line that passes through the given point and is (a) parallel

When the lines are parallel, they have same slope. So, slope of required line: m = -2

Using slope m =-2 and point(4,3) we can find y-intercept b

y=mx+b\\3=-2(4)+b\\3=-8+b\\b=3+8\\b=11

The equation of line will be:

y=mx+b\\y=-2x+11

Equation of the line that passes through the given point and is (a) parallel is: \mathbf{y=-2x+11}

Part b)

Write an equation of the line that passes through the given point and is (b) perpendicular

When the lines are perpendicular they have opposite slope. So, slope of required line: m = 1/2

Using slope m =1/2 and point(4,3) we can find y-intercept b

y=mx+b\\3=\frac{1}{2}(4)+b\\3=2+b\\b=3-2\\b=1

The equation of line will be:

y=mx+b\\y=\frac{1}{2}x+1

Equation of the line that passes through the given point and is (b) perpendicular is: \mathbf{y=\frac{1}{2}x+1}

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