Question 1

Solve. Provide answers in interval notation.
-$(x-8)(x+9)>0$

Accepted Answer

The inequality $(x-8)(x+9)>0$ is satisfied when either both factors are positive or both are negative. This happens for $x < -9$ or $x > 8$, leading to the solution $(-\infty,-9) \cup(8, \infty)$.

Question 2

Solve. Provide answers in interval notation.
-$(x+2)(x-5)<0$

Accepted Answer

The inequality $(x+2)(x-5)<0$ is satisfied when one factor is positive and the other is negative. This occurs when $x$ is between the roots $x=-2$ and $x=5$, hence the solution is $(-2,5)$.

Question 3

Solve. Provide answers in interval notation.
-$(x+3)(x+2) \leq 0$

Accepted Answer

The product $(x+3)(x+2) \leq 0$ is non-positive when one factor is non-positive and the other is non-negative. This occurs between the roots $x = -3$ and $x = -2$, inclusive, hence the interval $[-3,-2]$.

Question 4

Solve. Provide answers in interval notation.
-$49-x^{2} \geq 0$

Accepted Answer

The inequality $49-x^{2} \geq 0$ can be rewritten as $(7-x)(7+x) \geq 0$, which holds true for $x$ in the interval $[-7,7]$, including the endpoints, because $x^2$ must be less than or equal to $49$ for the inequality to hold.

Question 5

Solve. Provide answers in interval notation.
-$36-x^{2} \leq 0$

Accepted Answer

The answer of Solve. Provide answers in interval notation.
-\(36-x^{2} \leq...

Question 6

Solve. Provide answers in interval notation.
-$x^{2}+5 x-6>0$

Accepted Answer

First, factor the quadratic equation: $x^2 + 5x - 6 = (x + 6)(x - 1)$. The roots are $x = -6$ and $x = 1$. To determine where the expression is greater than zero, test values in each interval divided by the roots: less than -6, between -6 and 1, and greater than 1. The expression is positive in the intervals $(-\infty, -6)$ and $(1, \infty)$, making the correct answer $(-\infty, -6) \cup (1, \infty)$.

Question 7

Solve. Provide answers in interval notation.
-$x^{2}-5 x-14<0$

Accepted Answer

To solve the inequality $x^{2}-5x-14<0$, we first find the roots of the equation $x^{2}-5x-14=0$. Factoring the quadratic equation gives $(x-7)(x+2)=0$, which has roots at $x=7$ and $x=-2$. Plotting these roots on a number line and testing intervals, we find that the inequality is satisfied for $x$ values between -2 and 7, hence the solution in interval notation is $(-2,7)$.

Question 8

Solve. Provide answers in interval notation.
-$x^{2}-5 x-14 \leq 0$

Accepted Answer

To solve the quadratic inequality $x^{2}-5x-14 \leq 0$, first factor the quadratic equation: $(x-7)(x+2) \leq 0$. The roots are $x = 7$ and $x = -2$. The inequality is satisfied between these two roots, including the roots themselves, hence the solution in interval notation is $[-2, 7]$.

Question 9

Solve. Provide answers in interval notation.
-$x^{2}+11 x+28 \geq 0$

Accepted Answer

To solve the quadratic inequality $x^{2}+11x+28 \geq 0$, first factor the quadratic expression. It factors as $(x+7)(x+4) \geq 0$. The roots of the equation are $x = -7$ and $x = -4$. To determine the intervals where the inequality holds, consider the sign of the product in each interval determined by these roots: $(-\infty, -7)$, $(-7, -4)$, and $(-4, \infty)$. Testing points in each interval shows that the product is non-negative outside the roots, thus the solution is $(-\infty,-7] \cup[-4, \infty)$.

Question 10

Solve. Provide answers in interval notation.
-$x^{2}-8 x+16<0$

Accepted Answer

The given inequality $x^{2}-8x+16<0$ can be factored as $(x-4)^2<0$. Since a square of a real number is always non-negative, $(x-4)^2$ is always greater than or equal to 0. Therefore, there are no real values of $x$ for which $(x-4)^2<0$, indicating that there is no solution to the inequality.

Question 11

Solve. Provide answers in interval notation.
-$x^{2}-10 x+25 \geq 0$

Accepted Answer

The answer of Solve. Provide answers in interval notation.
-\(x^{2}-10 x+25...

Question 12

Solve. Provide answers in interval notation.
-$x^{2}-4 x \leq-3$

Accepted Answer

The answer of Solve. Provide answers in interval notation.
-\(x^{2}-4 x...

Question 13

Solve. Provide answers in interval notation.
-$(a-1)(a-3)(a-6)>0$

Accepted Answer

The answer of Solve. Provide answers in interval notation.
-$(a-1)(a-3)(a-6)>0$
...

Question 14

Solve. Provide answers in interval notation.
-$(b+5)(b+3)(b-2)<0$

Accepted Answer

The given inequality $(b+5)(b+3)(b-2)<0$ has critical points at $b=-5$, $b=-3$, and $b=2$. Testing intervals around these points, we find that the inequality is satisfied for $b$ in the intervals $(-\infty,-5)$ and $(-3,2)$.

Question 15

Solve. Provide answers in interval notation.
-$(\mathrm{c}+8)(\mathrm{c}-1)(\mathrm{c}-5)>0$

Accepted Answer

To solve the inequality $(\mathrm{c}+8)(\mathrm{c}-1)(\mathrm{c}-5)>0$, we find the zeros of the polynomial, which are $\mathrm{c}=-8$, $\mathrm{c}=1$, and $\mathrm{c}=5$. These values divide the number line into four intervals: $(-\infty, -8)$, $(-8, 1)$, $(1, 5)$, and $(5, \infty)$. Testing values from each interval in the inequality shows that the inequality is satisfied for $(-8, 1)$ and $(5, \infty)$, hence the solution in interval notation is $(-8,1) \cup(5, \infty)$.

Question 16

Solve. Provide answers in interval notation.
-$(x+9)(x-5)(x+2)>0$

Accepted Answer

To solve the inequality $(x+9)(x-5)(x+2)>0$, we find the zeros at $x=-9$, $x=5$, and $x=-2$. Plotting these on a number line and testing intervals gives us the solution $(-9,-2) \cup(5, \infty)$.

Question 17

Solve. Provide answers in interval notation.
-$(x-8)(x-10)(x+5)<0$

Accepted Answer

The correct intervals are found by solving the inequality $(x-8)(x-10)(x+5)<0$. The critical points are $x = -5$, $x = 8$, and $x = 10$. Testing values between and outside these points shows that the function is negative in the intervals $(-\infty,-5)$ and $(8,10)$.

Question 18

Graph the inequality.
-

Accepted Answer

The answer of Graph the inequality.
- 
...

Question 19

Graph the inequality.
-

Accepted Answer

The answer of Graph the inequality.
-
...

Question 20

Graph the inequality.
-

Accepted Answer

The answer of Graph the inequality.
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...

Quiz 16: Converting Units of Measurement

Solve. Provide answers in interval notation. - $(x-8) (x+9) >0$

Solve. Provide answers in interval notation. - $(x+2) (x-5) <0$

Solve. Provide answers in interval notation. - $(x+3) (x+2) \leq 0$

Solve. Provide answers in interval notation. - $49-x^{2} \geq 0$

Solve. Provide answers in interval notation. - $36-x^{2} \leq 0$

Solve. Provide answers in interval notation. - $x^{2}+5 x-6>0$

Solve. Provide answers in interval notation. - $x^{2}-5 x-14<0$

Solve. Provide answers in interval notation. - $x^{2}-5 x-14 \leq 0$

Solve. Provide answers in interval notation. - $x^{2}+11 x+28 \geq 0$

Solve. Provide answers in interval notation. - $x^{2}-8 x+16<0$

Solve. Provide answers in interval notation. - $x^{2}-10 x+25 \geq 0$

Solve. Provide answers in interval notation. - $x^{2}-4 x \leq-3$

Solve. Provide answers in interval notation. - $(a-1) (a-3) (a-6) >0$

Solve. Provide answers in interval notation. - $(b+5) (b+3) (b-2) <0$

Solve. Provide answers in interval notation. - $(\mathrm{c}+8) (\mathrm{c}-1) (\mathrm{c}-5) >0$

Solve. Provide answers in interval notation. - $(x+9) (x-5) (x+2) >0$

Solve. Provide answers in interval notation. - $(x-8) (x-10) (x+5) <0$

Graph the inequality. -

Graph the inequality. -

Graph the inequality. -

Quiz 16: Converting Units of Measurement

Solve. Provide answers in interval notation. - (x−8) (x+9) >0(x-8) (x+9) >0(x−8) (x+9) >0

Solve. Provide answers in interval notation. - (x+2) (x−5) <0(x+2) (x-5) <0(x+2) (x−5) <0

Solve. Provide answers in interval notation. - (x+3) (x+2) ≤0(x+3) (x+2) \leq 0(x+3) (x+2) ≤0

Solve. Provide answers in interval notation. - 49−x2≥049-x^{2} \geq 049−x2≥0

Solve. Provide answers in interval notation. - 36−x2≤036-x^{2} \leq 036−x2≤0

Solve. Provide answers in interval notation. - x2+5x−6>0x^{2}+5 x-6>0x2+5x−6>0

Solve. Provide answers in interval notation. - x2−5x−14<0x^{2}-5 x-14<0x2−5x−14<0

Solve. Provide answers in interval notation. - x2−5x−14≤0x^{2}-5 x-14 \leq 0x2−5x−14≤0

Solve. Provide answers in interval notation. - x2+11x+28≥0x^{2}+11 x+28 \geq 0x2+11x+28≥0

Solve. Provide answers in interval notation. - x2−8x+16<0x^{2}-8 x+16<0x2−8x+16<0

Solve. Provide answers in interval notation. - x2−10x+25≥0x^{2}-10 x+25 \geq 0x2−10x+25≥0

Solve. Provide answers in interval notation. - x2−4x≤−3x^{2}-4 x \leq-3x2−4x≤−3

Solve. Provide answers in interval notation. - (a−1) (a−3) (a−6) >0(a-1) (a-3) (a-6) >0(a−1) (a−3) (a−6) >0

Solve. Provide answers in interval notation. - (b+5) (b+3) (b−2) <0(b+5) (b+3) (b-2) <0(b+5) (b+3) (b−2) <0

Solve. Provide answers in interval notation. - (c+8) (c−1) (c−5) >0(\mathrm{c}+8) (\mathrm{c}-1) (\mathrm{c}-5) >0(c+8) (c−1) (c−5) >0

Solve. Provide answers in interval notation. - (x+9) (x−5) (x+2) >0(x+9) (x-5) (x+2) >0(x+9) (x−5) (x+2) >0

Solve. Provide answers in interval notation. - (x−8) (x−10) (x+5) <0(x-8) (x-10) (x+5) <0(x−8) (x−10) (x+5) <0

Graph the inequality. -

Graph the inequality. -

Graph the inequality. -

Solve. Provide answers in interval notation. - $(x-8) (x+9) >0$

Solve. Provide answers in interval notation. - $(x+2) (x-5) <0$

Solve. Provide answers in interval notation. - $(x+3) (x+2) \leq 0$

Solve. Provide answers in interval notation. - $49-x^{2} \geq 0$

Solve. Provide answers in interval notation. - $36-x^{2} \leq 0$

Solve. Provide answers in interval notation. - $x^{2}+5 x-6>0$

Solve. Provide answers in interval notation. - $x^{2}-5 x-14<0$

Solve. Provide answers in interval notation. - $x^{2}-5 x-14 \leq 0$

Solve. Provide answers in interval notation. - $x^{2}+11 x+28 \geq 0$

Solve. Provide answers in interval notation. - $x^{2}-8 x+16<0$

Solve. Provide answers in interval notation. - $x^{2}-10 x+25 \geq 0$

Solve. Provide answers in interval notation. - $x^{2}-4 x \leq-3$

Solve. Provide answers in interval notation. - $(a-1) (a-3) (a-6) >0$

Solve. Provide answers in interval notation. - $(b+5) (b+3) (b-2) <0$

Solve. Provide answers in interval notation. - $(\mathrm{c}+8) (\mathrm{c}-1) (\mathrm{c}-5) >0$

Solve. Provide answers in interval notation. - $(x+9) (x-5) (x+2) >0$

Solve. Provide answers in interval notation. - $(x-8) (x-10) (x+5) <0$