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2 years ago

Solve for x in the following inequality: 3(-2x - 4) > 18

Mathematics

2 answers:

grigory [225]2 years ago

7 0

Answer:

$\boxed {\boxed {\sf x< -5}}$

Step-by-step explanation:

We are asked to solve the following inequality for x.

$3(-2x-4) > 18$

Solve for x by isolating it and performing the inverse operations.

3 is being multiplied by (-2x-4). The inverse operation of multiplication is division. Divide both sides of the inequality by 3.

$\frac {3(-2x-4)}{3} > \frac{18}{3}$

$(-2x-4) > \frac{18}{3}$

$-2x-4 > 6$

4 is being subtracted from -2x. The inverse operation of subtraction is addition. Add 4 to both sides of the inequality.

$-2x-4+4 > 6+4 \\$

$-2x > 10$

x is being multiplied by -2. The inverse operation of multiplication is division. Divide both sides by -2.

$\frac {-2x}{-2} > \frac {10}{-2}$

$x> \frac {10}{-2}$

Since we divided by a negative number, the inequality sign must be flipped.

$x< \frac{10}{-2}$

$x < -5$

Schach [20]2 years ago

3 0

Answer:

x < -5

Step-by-step explanation:

3 ( -2x - 4 ) > 18

→ Expand the brackets

-6x - 12 > 18

→ Add 12 to both sides

-6x > 30

→ Divide both sides by -6

x < -5

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3 years ago

A florist sold 14 flower bouquets yesterday, including 7 lily bouquets. Based on past data, how many of the next 20 bouquets sol

tensa zangetsu [6.8K]

Answer:

Step-by-step explanation:

From past data:

Fraction of lily sold :

Total flowers / number of lily

Total flowers = 14

Number of lily = 7

Fraction of lily = 14 /7 = 1/2

Going by these ;

Expected number of lilies in the next 20 bouquets sold :

Fraction of lily * number of flower in bouquet

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5 0

3 years ago

The graph shows the functions f(x), p(x), and g(x): Graph of function g of x is y is equal to 1 plus the quantity 1.5 raised to

satela [25.4K]

Part A:

Given that the straight line p(x) joins the ordered pairs (0, 2) and (1, -5), thus the equation of the line joining ordered pairs (0, 2) and (1, -5) is given by

$\frac{y-2}{x} = \frac{-5-2}{1} =-7 \\ \\ \Rightarrow y-2=-7x \\ \\ \Rightarrow y=-7x+2$

Thus, p(x) = -7x + 2

Given that the straight line f(x) joins the ordered pairs (4, 1) and (2, -3), thus the equation of the line joining ordered pairs (4, 1) and (2, -3) is given by

$\frac{y-1}{x-4} = \frac{-3-1}{2-4} =\frac{-4}{-2}=2 \\ \\ \Rightarrow y-1=2(x-4)=2x-8 \\ \\ \Rightarrow y=2x-7$

Thus, f(x) = 2x - 7

The solution to the pair of equations represented by p(x) and f(x) is given by

p(x) = f(x)
⇒ -7x + 2 = 2x - 7
⇒ -7x - 2x = -7 - 2
⇒ -9x = -9
⇒ x = -9 / -9 = 1

Substituting for x into p(x), we have

p(1) = -7(1) + 2 = -7 + 2 = -5

Therefore, the solution to the pair of equations represented by p(x) and f(x) is (1, -5)

Part B:

From part A, we have that f(x) = 2x - 7

when x = -8

f(-8) = 2(-8) - 7 = -23

Thus, (-8, -23) is a solution to f(x).

When x = -10

f(-10) = 2(-10) - 7 = -27

Thus, (-10, -27) is a solution to f(x).

Therefore, two solutions of f(x) are (-8, -23) and (-10, -27).

Part C:

From part A, we have that p(x) = -7x + 2, given that $g(x) = 1 + 1.5^x$

From the graphs of p(x) and g(x), we can see that the two graphs intersected at the point (0, 2).

Therefore, the solution to the equation p(x) = g(x) is (0, 2).

3 0

4 years ago