All categories

3 years ago

12x−39≤9 AND−4x+3<−6

Mathematics

2 answers:

nignag [31]3 years ago

8 0

Answer:

2 1/4 < x ≤ 4

Step-by-step explanation:

12x−39≤9 AND−4x+3<−6

Solve them separately and then put back together

12x−39≤9

Add 39 to each side

12x−39+39≤9+39

12x ≤48

Divide by 12

12x/12 ≤48/12

x ≤4

Now the other inequality

−4x+3<−6

Subtract 3 from each side

−4x+3-3<−6-3

-4x < -9

Divide by -4, remembering to flip the inequality

-4x/-4 > -9/-4

x > 2 1/4

put back together

x > 2 1/4 and x ≤4

2 1/4 < x ≤ 4

densk [106]3 years ago

5 0

Answer:

2.25<x≤4

Step-by-step explanation:

12x−39≤9 ⇒ 12x≤ 48 ⇒ x≤4

−4x+3<−6 ⇒ -4x < -9 ⇒ x> 9/4= 2.25

2.25<x≤4

x= (2.25, 4]

You might be interested in

What is x over 5 - 68 = -95

vagabundo [1.1K]

Hello, there!

This would look like: x/5 - 68 = -95

First, we want to isolate the x.

x/5 - 68 = -95
+68 +68

x/5 = -27

Now, we will work backwards to find the x.

-27 * 5 = x

-27 * 5 = -135

x = -135

Your answer is -135

I hope I helped!

Let me know if you need anything else!

~ Zoe

5 0

3 years ago

Q8 Q3.) Solve the system by the substitution method.

inn [45]

Recall that $(x+y)^2=x^2+2xy+y^2$ . So we can add twice the first equation to the second one to get

$x^2+y^2+2xy=10+2\cdot3\iff(x+y)^2=16\implies x+y=\pm4$

Since $xy=3$ , we have $y=\dfrac3x$ $(x\neq0)$ so

$x+y=x+\dfrac3x=\pm4\implies x^2\mp4x+3=0$

If $x+y=4$ , then

$x^2-4x+3=(x-3)(x-1)=0\implies x=3,x=1\implies y=1,y=3$

If $x+y=-4$ , then

$x^2+4x+3=(x+1)(x+3)=0\implies x=-1,x=-3\implies y=-3,y=-1$

So the solution set is

$(x,y)\in\{(-3,1),(1,3),(-1,-3),(-3,-1)\}$

3 0

3 years ago

What is the simplified form of the following expression? 8ab/-4b

kondaur [170]

-2a

Step-by-step explanation:

steps:1. first write the question again : 8ab/-4b

2.first 8 divide by -4=-2

3.write ' a' with -2because u don't have another 'a' down belowso that u can pair it up and cancel

so: -2a.

4. cancel 'b' on top and 'b' at the bottom.

3 0

3 years ago

If f'(x) = 0 at x = -2, 0, and 2

Sedbober [7]

Answer:

12345678754324567876

5 0

2 years ago

A house on the market was valued at $245,000. After several years, the value increased by 9%. By how much did the house's value

aniked [119]

We are given that a house had a value of $245000 and its value was increased by 9%. To determine how much is this value increase in dollars we need to multiply the value of the house by 9/100. We get this:

$245000\times\frac{9}{100}=22050$

Therefore, the increase in dollars is $22050. Now, to determine the current value we need to add the increase to the previous value, we get:

$245000+22050=267050$

Therefore, the current value of the house is $267050.

6 0

1 year ago