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Question

Solve for $$x$$:
$$\cfrac { x-4 }{ 7 } -\cfrac { x+4 }{ 5 } =\cfrac { x+3 }{ 7 } $$


Solution

Given, $$\dfrac { x-4 }{ 7 } -\dfrac { x+4 }{ 5 } =\dfrac { x+3 }{ 7 } $$

$$\Rightarrow$$ $$\dfrac { 5(x-4)-7(x+4) }{ 35 } =\dfrac { x+3 }{ 7 } $$ ....[Cross-multiplying the denominators on the LHS]

$$\Rightarrow$$ $$\dfrac{5x-20-7x-28}{35}=\dfrac { x+3 }{ 7 } $$  ...[By Distribution Law]

$$\Rightarrow$$ $$\dfrac{-2x-48}{35}=\dfrac { x+3 }{ 7 } $$  ...[On simplifying]

$$\Rightarrow$$ $$-2x-48=\dfrac { x+3 }{ 7 } \times 35$$

$$\Rightarrow$$ $$-2x-48=(x+3)\times 5$$

$$\Rightarrow$$ $$-2x-48=5x+15$$   ...[By Distribution Law]

$$\Rightarrow$$ $$-2x-5x=15+48$$  ...[Transposing $$x$$ terms to one side]

$$\Rightarrow$$ $$-7x=63$$  ...[On simplifying]

$$\Rightarrow$$ $$x=\dfrac{63}{-7}=-9$$.

Mathematics

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