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3 years ago

Solve the equation. 2/3 - 4x 7/2= -9x+ 5/6 step by step

Mathematics

2 answers:

Lostsunrise [7]3 years ago

6 0

Answer: $\bold{x=\dfrac{11}{21}}$

Step-by-step explanation:

$\dfrac{2}{3}-\dfrac{4x+7}{2}=-9x+\dfrac{5}{6}\\\\(6)\dfrac{2}{3}-(6)\dfrac{4x+7}{2}=-9x(6)+(6)\dfrac{5}{6}\qquad \text{(multiplied by LCD) }\\\\4 - 12x-21=-54x+5\qquad \text{(simplified)}\\\\-12x - 17 = -54x + 5\qquad \text{(added like terms)}\\\\42x-17=5\qquad \text{(added 54x to both sides)}\\\\42x = 22\qquad \text{(added 17 to both sides)}\\\\x=\dfrac{22}{42}\qquad \text{(divided both sides by 42)}\\\\x=\dfrac{11}{21}\qquad \text{(reduced the fraction)}$

NOTE: The sign between 4x and 7 is missing in the question you posted. I assumed it was 4x + 7 in order to solve the equation.

nataly862011 [7]3 years ago

6 0

Answer:

X=-2/3

Step-by-step explanation:

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Georgia [21]

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What are the domain and range of the inequality y < sqrt x+3+1

love history [14]

Given:

The inequality is:

$y$

To find:

The domain and range of the given inequality.

Solution:

We have,

$y$

The related equation is:

$y=\sqrt{x+3}+1$

This equation is defined if:

$x+3\geq 0$

$x\geq -3$

In the given inequality, the sign of inequality is <, it means the points on the boundary line are not included in the solution set. Thus, -3 is not included in the domain.

So, the domain of the given inequality is x>-3.

We know that,

$\sqrt{x+3}\geq 0$

$\sqrt{x+3}+1\geq 0+1$

$y\geq 1$

The points on the boundary line are not included in the solution set. Thus, 1 is not included in the range.

So, the domain of the given inequality is y>1.

Therefore, the correct option is A.

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