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2 years ago

Solve the following inequality. Use interval notation.

Mathematics

1 answer:

Svetach [21]2 years ago

8 0

9514 1404 393

Answer:

(-∞, -1/3) U (3, ∞)

Step-by-step explanation:

The given inequality is equivalent to two inequalities (joined with OR).

-(3x -4) +3 ≥ 8

-3x +7 ≥ 8 . . . . . . eliminate parentheses

-3x ≥ 1 . . . . . . . subtract 7

x ≤ -1/3 . . . . . divide by 3

3x -4 +3 ≥ 8

3x ≥ 9 . . . . . add 1

x ≥ 3 . . . . . . divide by 3

Then the solution to the inequality is the union of these intervals:

x ∈ (-∞, -1/3) ∪ (3, ∞)

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earnstyle [38]

Answer:

$3.14 \times 10 ^{3} < 2.6 \times 10^{3}$

Step-by-step explanation:

$3.14 \times 10 ^{3}$

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2 years ago

67. The line contains the point (4,0) and is parallel to the line defined by 3x = 2y.

olganol [36]

Answer:

$y=\frac{3}{2} x-6$

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form:

$y=mx+b$ where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)

Parallel lines will always have the same slope but different y-intercepts.

1) Determine the slope of the parallel line

Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.

$3x = 2y$

Switch the sides

$2y=3x$

Divide both sides by 2 to isolate y

$\frac{2y}{2} = \frac{3}{2} x\\y=\frac{3}{2} x$

Now that this equation is in slope-intercept form, we can easily identify that $\frac{3}{2}$ is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope $\frac{3}{2}$ . Plug this into $y=mx+b$ :