Question

Solve the equation -3(x - 14) + 9x = 6x + 42. Does the equation have one solution, no solution, or infinitely many solutions?

Answer 1

Hello!

$\large\boxed{\text{Infinitely many solutions.}}$

-3(x - 14) + 9x = 6x + 42

Distribute the coefficient of the parenthesis:

-3(x) - 3(-14) + 9x = 6x + 42

-3x + 42 + 9x = 6x + 42

Combine like terms:

6x + 42 = 6x + 42

Both sides of the equation are the same, therefore:

There are infinitely many solutions.

Answer 2

AnswEr :

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• Equation have Infinitely many Solutions

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➤ How to solve ?

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For solving such problems we need to recall equations .

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When the value of two variable comes equal and zero in an equation then that equation is said to have infinitely many solutions . If the value of a variable have any particular constant then the equation is said to have one solution . If the value of of any variable comes undefine then the equation is said to have no solution .

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SolutiOn :

➠ - 3 ( x - 14 ) + 9x = 6x + 42

➠ -3x + 42 + 9x = 6x + 42

Now, we will bring the variable on left hand side and constants on right hand side

➠ -3x + 9x - 6x = 42 - 42

➠ -9x + 9x = 42 - 42

➠ 0 = 42 - 42

➠ 0 = 0

As we can see the equation have end with a zero the equation have indefinitely many solutions

➠ Indefinity many solutions

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