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2 years ago

Solve the equation -2 = 3x/5 + 1

Mathematics

1 answer:

kirill [66]2 years ago

4 0

$- 2 = \dfrac{3x}{5} + 1 | \times 5 \\ - 10 = 3x + 5 \\ - 3x = 15 | \div ( - 3) \\ x = - 5$

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Andreas93 [3]

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3 years ago

Which expression is equivalent to (5g^4+5g^3-17g^2+6g)-(3g^4+6g^3-7g^2-12)/g+2

ankoles [38]

Option C:

$2 g^{3}-5 g^{2}+6$

Solution:

Given expression:

$$\frac{\left(5 g^{4}+5 g^{3}-17 g^{2}+6 g\right)-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right)}{g+2}$

To find which expression is equal to the given expression.

$$\frac{\left(5 g^{4}+5 g^{3}-17 g^{2}+6 g\right)-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right)}{g+2}$

Expand the term $-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right):-3 g^{4}-6 g^{3}+7 g^{2}+12$

$$=\frac{5 g^{4}+5 g^{3}-17 g^{2}+6 g- 3 g^{4}-6 g^{3}+7 g^{2}+12}{g+2}$

Arrange the like terms together.

$$=\frac{5 g^{4}- 3 g^{4}+5 g^{3}-6 g^{3}-17 g^{2}+7 g^{2}+6 g+12}{g+2}$

$$=\frac{2 g^{4}- g^{3}-10 g^{2}+6 g+12}{g+2}$

Factor the numerator $2 g^{4}-g^{3}-10 g^{2}+6 g+12=(g+2)\left(2 g^{3}-5 g^{2}+6\right)$

$$=\frac{(g+2)\left(2 g^{3}-5 g^{2}+6\right)}{g+2}$

Cancel the common factor g + 2, we get

$=2 g^{3}-5 g^{2}+6$

Hence option C is the correct answer.

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