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3 years ago

Solve for x −9x+5≤17 OR 13x+25≤−1

Mathematics

2 answers:

Lesechka [4]3 years ago

4 0

Answer:

$(-\infty,-2] \cup [\displaystyle\frac{-4}{3},-\infty)$

Step-by-step explanation:

We are given the following information in the question:

We have to solve the given inequalities for x:

Inequality 1

$-9x+5 \leq 17\\-9x \leq 17-5\\-9x \leq 12\\\\x \leq \displaystyle\frac{12}{-9}\\\\x \geq \frac{-4}{3}\\\\x \in [\frac{-4}{3},-\infty)$

Inequality 2

$13x + 25 \leq -1\\13x \leq -1-25\\13x \leq -26\\\\x \leq \displaystyle\frac{-26}{13}\\\\x \leq -2\\x \in (-\infty,-2]$

The combined solution for both the inequalities is given by:

$(-\infty,-2] \cup [\displaystyle\frac{-4}{3},-\infty)$

arsen [322]3 years ago

3 0

Answer:

(-∞ 2] ∪ [-4/3 ∞ )

Step-by-step explanation:

Given compound inequality,

$-9x+5\leq 17\text{ or }13x+25\leq -1$

$-9x\leq 12\text{ or }13x\leq -26$ ( Subtraction property of inequality )

$-x\leq \frac{12}{9}\text{ or }x\leq -\frac{26}{13}$ ( Division property of inequality )

$-x\leq \frac{4}{3}\text{ or }x\leq -2$

$x\geq -\frac{4}{3}\text{ or }x\leq -2$ ( a - b )

Hence, the solution of the given inequality is,

(-∞ -2] ∪ [-4/3 ∞ )

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Write the equation of the line that passes through the points (1, -6) and (8, 9). Put

ZanzabumX [31]

Answer:

$y-9 = \frac{15}{7} (x-8)$

Step-by-step explanation:

Point-slope form is represented by $y-y_1 = m (x-x_1)$ . To write an equation with it, we need the slope of the line and a point the line crosses through. We already have at least one point the line crosses through, so let's figure out the slope.

To find the slope, use the slope formula $\frac{y_2-y_1}{x_2-x_1}$ . $x_1$ and $y_1$ represent the x and y values of one point the line crosses, and $x_2$ and $y_2$ represent the x and y values of another point the line crosses. So, using the x and y values of (1, -6) and (8, 9), substitute them into the formula and solve:

$\frac{(9)-(-6)}{(8)-(1)} \\= \frac{9+6}{8-1} \\= \frac{15}{7}$

Thus, the slope is $\frac{15}{7}$ .

2) Now, using the point-slope form of $y-y_1 = m (x-x_1)$ , substitute $m$ , $x_1$ , and $y_1$ for real values in order to write an equation in point-slope form. The $m$ represents the slope, so substitute $\frac{15}{7}$ in its place. The $x_1$ and $y_1$ represent the x and y values of one point on the line. So, choose any one of the points given - either one is fine - and substitute its x and y values for $x_1$ and $y_1$ . (I chose (8,9)). This gives the following equation and answer: