What value of x is in the solution set of 2(3x – 1) ≥ 4x – 6?

1 answer:

4 0

2(3x - 1) ≥ 4x - 6 Remove the brackets on the left.
6x - 2 ≥ 4x - 6 Subtract 4x from both sides.
6x - 4x - 2 ≥ - 6 combine like terms on the left.
2x - 2 ≥ - 6 Add 2 to both sides
2x ≥ - 6+ 2
2x ≥ -4 Divide by 2
x ≥ - 4/2
x ≥ - 2 answer <<<<<<<<

Check
2(3*-2 - 1) ≥ 4x - 6
2(-6 - 1) ≥ 4(-2) - 6
2(-7) ≥- 8 - 6
- 14 = - 14 and this checks.

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The Cartesian coordinate of a point in the xy plane are (x,y)=(-3.50,-2.50)m. Find the poler coordinate of this point

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The polar coordinate of $P(x,y) = (-3.50\,m,-2.50\,m)$ is $P (r,\theta) = (4.301\,m, 215.538^{\circ})$ .

Explanation:

Given a point in rectangular form, that is $P(x,y) = (x,y)$ , its polar form is defined by:

$P(x,y) = (r,\theta)$ (1)

Where:

$r$ - Norm, measured in meters.

$\theta$ - Direction, measured in sexagesimal degrees.

The norm of the point is determined by Pythagorean Theorem:

$r = \sqrt{x^{2}+y^{2}}$ (2)

And direction is calculated by following trigonometric relation:

$\theta = \tan^{-1} \frac{y}{x}$ (3)

If we know that $x = -3.50\,m$ and $y = -2.50\,m$ , then the components of coordinates in polar form is:

$r = \sqrt{(-3.50\,m)^{2}+(-2.50\,m)^{2}}$

$r \approx 4.301\,m$

Since $x < 0\,m$ and $y < 0\,m$ , direction is located at 3rd Quadrant. Given that tangent function has a period of 180º, we find direction by using this formula: