Solve the inequality for x. Show each step of the solution. 12x>9(2x-3)-15

Mathematics

1 answer:

valina [46]3 years ago

5 0

$12x > 9(2x-3)-15\qquad|\text{use distributive property}\\\\12x > (9)(2x)+(9)(-3)-15\\\\12x > 18x-27-15\\\\12x > 18x-42\qquad|\text{subtract 18x from both sides}\\\\-6x > -42\qquad|\text{change the signs}\\\\6x < 42\qquad|\text{divide both sides by 6}\\\\x < 7$

You might be interested in

Enter the correct answer in the box. Write your answer in the form y = mx + b, using the appropriate inequality symbol in place

Afina-wow [57]

Step-by-step explanation:

the delimiter line is going through the points (-4, 0) and (0, -4).

the line function

y = mx + b

m is the slope of the line, b is the y-intercept (the y value when x = 0).

the slope is the ratio of "y coordinate change / x coordinate change" when going from one point to another.

so, for the 2 found points :

x changes by +4 (from -4 to 0)

y changes by -4 (from 0 to -4).

the slope m is then

-4/+4 = -1

and the y-intercept is -4 (as explained).

so, the line is

y = -x - 4

and the graphic says that all values greater than our equal to the line values are valid, so

y >= -x - 4

7 0

2 years ago

Read 2 more answers

What is the value of g^-1(9)

mars1129 [50]

Hi there!

• g(x) = 6x - 3

Then,
if g(x) = y :-

y = 6x - 3

⇒6x = y + 3

⇒x = $\dfrac{\text{y} + 3}{6}$

According to th' question :-

g⁻¹(x) = $\dfrac{\text{x} + 3}{6}$

g⁻¹(9) = $\dfrac{9 + 3}{6}$

g⁻¹(9) = $\dfrac{12}{6}$

g⁻¹(9) = 2

Hence,
The required answer is g⁻¹(9) = 2

~ Hope it helps!

3 0

3 years ago

Read 2 more answers

What is the y-intercept of function g if g(x) = 2f(x) + 1 ?

Vadim26 [7]

Answer:

D. (0,1)

Step-by-step explanation:

Hope it helps ;)

4 0

3 years ago

Read 2 more answers