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3 years ago

Solve for x in this inequality. Show all your work and graph your solution. 4(x-3)<2x-4

Mathematics

1 answer:

maw [93]3 years ago

6 0

Answer:

x<4

Step-by-step explanation:

To solve for x in the inequality equation, the terms should be rearranged such that x is on one side and integers are on the other side.

First, expand 4(x-3).

This will obtain:

$4x - 12 < 2x - 4$

Now, shift x terms and integers on each side.

$4x - 2x < - 4 + 12$

After simplifying, it will get:

$2x < 8$

Finally, we can solve for x.

$x < 4$

We can also draw the respective graph (please don't mind my drawings), where the area shaded in green is the range.

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ANSWER ASAP!! Find the area of a triangle with legs that are: 12 m, 15 m, and 9 m.

Setler79 [48]

Answer:

Step-by-step explanation:

<h3>METHOD 1:</h3>

You can use the Heron's formula:

$A=\sqrt{p(p-a)(p-b)(p-c)}$

where

<em>p</em><em> - half of perimeter</em>

<em>a, b, c</em><em> - lengths of sides</em>

We have

$a=12m;\ b=15m;\ c=9m$

Calculate:

$p=\dfrac{12+15+9}{2}=\dfrac{36}{2}=18\ (m)\\\\A=\sqrt{18(18-12)+(18-15)(18-9)}\\\\A=\sqrt{(18)(6)(3)(9)}\\\\A=\sqrt{2916}\\\\A=54\ (m^2)$

<h3>METHOD 2:</h3>

Let's check that it is not a right triangle.

If the sum of the squares of the two shorter sides is equal to the square of the longest side, then this triangle is rectangular.

We have

$9m < 12m$

Check:

$9^2+12^2=81+144=225\\15^2=225$

This is a right trianglr wherew 9m and 12m are legs and 15m is a hypotenuse.

The formula of an area of a right triangle is:

$A=\dfrac{ab}{2}$

Substitute:

$A=\dfrac{(9)(12)}{2}=\dfrac{108}{2}=54\ (m^2)$

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What is the surface area of the cube?

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3 years ago

What is the solution to the system of equations below?

Alekssandra [29.7K]

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3 years ago

Match each equation with its solution set.

taurus [48]

Answer:

1- The solution of I2x + 5I = 9 is {-7 , 2}

2- The solution of I2x + 7I + 2 = 11 is {-8 , 1}

3- The solution of I5 - xI = 6 is {-1 , 11}

4- The solution of I6x - 8I + 7 = 5 is ∅

5- The solution of Ix + 3I = 12 is {-15 , 9}

6- The solution of Ix - 3I = -12 is ∅

Step-by-step explanation:

* At first lets explain the meaning of IxI = a

- If IxI = a ⇒ then x = a or x = -a

- IxI never give a negative answer, because IxI means the

magnitude of x is always positive

Ex: I-2I is 2

* Now lets find the solution of each equation

1- ∵ I2x + 5I = 9

∴ 2x + 5 = 9 ⇒ subtract 5 from both sides

∴ 2x = 4 ⇒ divide both sides by 2

∴ x = 2

∴ 2x + 5 = -9 ⇒ subtract 5 from both sides

∴ 2x = -14 ⇒ divide both sides by 2

∴ x = -7

* The solution of I2x + 5I = 9 is {-7 , 2}

2- ∵ I2x + 7I + 2 = 11 ⇒ Subtract 2 from both sides

∴ I2x + 7I = 9

∴ 2x + 7 = 9 ⇒ subtract 7 from both sides

∴ 2x = 2 ⇒ divide both sides by 2

∴ x = 1

∴ 2x + 7 = -9 ⇒ subtract 7 from both sides

∴ 2x = -16 ⇒ divide both sides by 2

∴ x = -8

* The solution of I2x + 7I + 2 = 11 is {-8 , 1}

3- ∵ I5 - xI = 6

∴ 5 -x = 6 ⇒ subtract 5 from both sides

∴ -x = 1 ⇒ divide both sides by -1

∴ x = -1

∴ 5 -x = -6 ⇒ subtract 5 from both sides

∴ -x = -11 ⇒ divide both sides by -1

∴ x = 11

* The solution of I5 - xI = 6 is {-1 , 11}

4- ∵ I6x - 8I + 7 = 5 ⇒ Subtract 7 from both sides

∴ I6x - 8I = -2

- I I never give negative answer

* The solution of I6x - 8I + 7 = 5 is ∅

5- ∵ Ix + 3I = 12

∴ x + 3 = 12 ⇒ subtract 3 from both sides

∴ x = 9

∴ x + 3 = -12 ⇒ subtract 3 from both sides

∴ x = -15

* The solution of Ix + 3I = 12 is {-15 , 9}

6- ∵ Ix - 3I = -12

- I I never give negative answer

* The solution of Ix - 3I = -12 is ∅

4 0

3 years ago