6 3x−8≤23 AND −4x+26≥63

Mathematics

1 answer:

Airida [17]1 year ago

8 0

The solution to the compound inequality given as 3x−8≤23 AND −4x+26≥63 is x ≤ 31/3 AND x ≤ -89/4

<h3>How to determine the solution to the compound inequality?</h3>

The compound inequality is given as:

3x−8≤23 AND −4x+26≥63

Rewrite properly as:

3x − 8 ≤ 23 AND −4x + 26 ≥ 63

Add to both sides of compound inequality ,the constant in the compound inequality expression

So, we have:

3x ≤ 31 AND −4x ≥ 89

Divide both sides of compound inequality, by the coefficient of the variable x in the compound inequality expression

So, we have:

x ≤ 31/3 AND x ≤ -89/4

hence, the solution to the compound inequality given as 3x−8≤23 AND −4x+26≥63 is x ≤ 31/3 AND x ≤ -89/4

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X2 - 6x + 12 and y = 2x - 4, algebraically are

olga_2 [115]

The solution is (4, 4)

Solution:

Given system of equations are:

$y = x^2 - 6x + 12 ------ eqn\ 1\\\\y = 2x - 4 ---------- eqn\ 2$

Substitute eqn 2 in eqn 1

$x^2 - 6x + 12 = 2x - 4$

Make the right side of equation 0

$x^2 - 6x + 12 - 2x + 4 = 0\\\\x^2 -8x + 16 = 0$

Solve by quadratic equation

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=-8,\:c=16:\\\\x=\frac{-\left(-8\right)\pm \sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:16}}{2\cdot \:1}\\\\x=\frac{-\left(-8\right)\pm \sqrt{0}}{2\cdot \:1}\\\\x = \frac{8}{2}\\\\x = 4$