Question

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

Answer 1

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

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

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

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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

$\longrightarrow{ \sf{ - 10 \times 11 + 17 \times 11 - 2}}$

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

$\longrightarrow{ \sf{77 - 2}}$

$\dashrightarrow{ \sf{75}}$

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 .

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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

~$\text{TheAnimeGirl}$

Answer 2

Ok here are the steps and the answer