Solve x*5=114 a*b=a*b-(a+b)

Evaluate

{x \times 5 = 114 ab 114 ab = ab - (a + b)

Use the commutative property to reorder the terms

{5 x = 114 ab 114 ab = ab - (a + b)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

{5 x = 114 ab 114 ab = ab - a - b

Solve the equation for x

More Steps

{x = \frac{114 ab}{5} 114 ab = ab - a - b

Substitute the given value of x into the equation 114 ab = ab - a - b

114 ab = ab - a - b

Evaluate

114 ba = ba - a - b

Collect like terms by calculating the sum or difference of their coefficients

114 ba = (b - 1) a - b

Move the variable to the left side

114 ba - (b - 1) a = - b

Subtract the terms

More Steps

(113 b + 1) a = - b

Divide both sides

\frac{( 113 b + 1 ) a}{113 b + 1} = \frac{- b}{113 b + 1}

Divide the numbers

a = \frac{- b}{113 b + 1}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

a = - \frac{b}{113 b + 1}

Substitute the given value of a into the equation x = \frac{114 ab}{5}

x = \frac{114 ( - \frac{b}{113 b + 1} ) b}{5}

Simplify the expression

x = - \frac{114 b ^{2}}{5 ( 113 b + 1 )}

Solution

(a, b, x) = (- \frac{b}{113 b + 1}, b, - \frac{114 b ^{2}}{5 ( 113 b + 1 )}), b \in R

Alternative Form

Infinitely many solutions

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