Solve for x: 3 2x=5x-9

Mathematics

1 answer:

atroni [7]3 years ago

4 0

3+2x=5x-9
minus 2x both sies
3=3x-9
add 9 to both sides
12=3x
divide both sides by 3
4=x

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An exponent signifies repeated multiplication.

$x\cdot x\cdot x=x^{3}$ the factor x is repeated 3 times

Exponents can be added and subtracted to express the effects of multiplication and division.

$\dfrac{x\cdot x\cdot x\cdot x\cdot x}{x\cdot x\cdot x}=\dfrac{x^{5}}{x^{3}}\\\\=\dfrac{x\cdot x\cdot x}{x\cdot x\cdot x}\cdot x\cdot x=x\cdot x\\\\=x^{(5-3)}=x^{2}$

The addition and subtraction of exponents works the same even when there are more denominator factors than numerator factors.

$\dfrac{x\cdot x\cdot x}{x\cdot x\cdot x\cdot x\cdot x}=\dfrac{x^{3}}{x^{5}}=\dfrac{1}{x^{2}}\\\\=x^{(3-5)}=x^{-2}$

That is, a negative numerator exponent is the same as a positive denominator exponent and vice versa. You can move a factor with an exponent from denominator to numerator and change the sign of the exponent, and vice versa.

Your expression has 3 in the denominator with a negative exponent. It can be moved to the numerator and the exponent changed to positive:

$\dfrac{1}{3^{-2}}=3^{2}\\\\=3\cdot 3=\bf{9}$