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3 years ago

3x+4=7-2x Solve this equation for x with steps

1 answer:

5 0

Simplifying
3x + 4 = 7 + -2x

Reorder the terms:
4 + 3x = 7 + -2x

Solving
4 + 3x = 7 + -2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2x' to each side of the equation.
4 + 3x + 2x = 7 + -2x + 2x

Combine like terms: 3x + 2x = 5x
4 + 5x = 7 + -2x + 2x

Combine like terms: -2x + 2x = 0
4 + 5x = 7 + 0
4 + 5x = 7

Add '-4' to each side of the equation.
4 + -4 + 5x = 7 + -4

Combine like terms: 4 + -4 = 0
0 + 5x = 7 + -4
5x = 7 + -4

Combine like terms: 7 + -4 = 3
5x = 3

Divide each side by '5'.
x = 0.6

Answer: x = 0.6

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a. The gradient is

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b. The gradient at point P(1, 2) is

$\boxed{\nabla f(1,2)=-8\,\vec\imath+12\,\vec\jmath}$

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It looks like

$\vec u=\dfrac{13}2\,\vec\imath+5\,\vec\jmath$

so that

$\|\vec u\|=\sqrt{\left(\dfrac{13}2\right)^2+5^2}=\dfrac{\sqrt{269}}2$

Then

$D_{\vec u}f(1,2)=\dfrac{\left(-8\,\vec\imath+12\,\vec\jmath\right)\cdot\left(\frac{13}2\,\vec\imath+5\,\vec\jmath\right)}{\frac{\sqrt{269}}2}$

$\boxed{D_{\vec u}f(1,2)=\dfrac{16}{\sqrt{269}}}$

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If (x-24)0.25 = 4, distribute 0.25 within the parenthesis.
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since the lengths of all those four sides are in a 3:2:6:7 ratio, and the whole perimeter is 126, what we do is, simply divide the whole by (3+2+6+7) and distribute accordingly.

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