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2 years ago

-1/2x + 6 < 4x - 3 i need to find the value of X with step-by-step explanation

Mathematics

2 answers:

Ray Of Light [21]2 years ago

8 0

Answer:

$\boxed{\boxed{\tt x>2}}$

Step-by-step explanation:

$\tt -\cfrac{1}{2}x+6$

Subtract 6 from both sides:

$\tt -\cfrac{1}{2}x+6-6$

$\tt -\cfrac{1}{2}x$

Now, subtract 4x from both sides:

$\tt -\cfrac{1}{2}x-4x$

$\tt -\cfrac{9}{2}x$

Multiply both sides by -1:

$\tt -\cfrac{9}{2}x\times -1$

$\tt \cfrac{9}{2}x>9$

Multiply both sides by 2:

$\tt 2\times \cfrac{9}{2}x>9\times \:2$

$\tt 9x>18$

Divide both sides by 9:

$\tt \cfrac{9x}{9}>\cfrac{18}{9}$

$\tt x>2$

____________________________

WITCHER [35]2 years ago

7 0

Answer:

x > 2

Step-by-step explanation:

-1/2x + 6 < 4x - 3

Start by adding 1/2x to both sides to get both x's on the same side

6 < 4 1/2x - 3

Add 3 to both sides to keep the x's by themselves on one side

9 < 4 1/2x

Divide both sides by 4 1/2 to get x by itself

2 < x so x > 2

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the equation for finding the slope of a line when given two points is $\frac{y_2-y_1}{x_2-x_1}$ , aka the change in y over the change in x.

pick one of your coordinate pairs to be $y_2\\$ and $x_2$ . it doesn't matter which coordinate pair you choose as long as you keep them as $y_2\\$ and $x_2$ . the remaining coordinate pair will be $y_1$ and $x_1$ .

for this example, i'll use (2, 10) for $y_2\\$ and $x_2$ and (6, 7) for $y_1$ and $x_1$ .

**before i begin, i just want to note that you can do these next four steps in any order that you want. i personally prefer to plug in my y-values first and then my x-values, but you can choose to instead plug in the values of each coordinate pair (like starting by plugging in the coordinate pair (2, 10) with 10 for $y_2\\$ and 2 for $x_2$ ). it's up to you. i'm going to explain the steps by plugging in my y-values first and then my x-values because that's the way i normally do it.

first, start by plugging in the y-value from the coordinate pair of your choosing in for $y_2\\$ . since i chose (2, 10) for $y_2\\$ and $x_2$ , i'll plug in 10 for $y_2\\$ .

$\frac{y_2-y_1}{x_2-x_1}$ ⇒ $\frac{10-y_1}{x_2-x_1}$

then plug in the remaining coordinate pair's y-value in for $y_1$ . since the coordinate pair that's left is (6, 7), i will plug in 7 for $y_1$ .

$\frac{y_2-y_1}{x_2-x_1}$ ⇒ $\frac{10-7}{x_2-x_1}$

now i'm going to plug in the x-values. i chose (2, 10) to plug in for $y_2\\$ and $x_2$ , so now i'll plug in 2 for $x_2$ .

$\frac{y_2-y_1}{x_2-x_1}$ ⇒ $\frac{10-7}{2-x_1}$

and all that's left to plug in is the x-value from (6, 7), so i will plug that in for $x_1$ .

$\frac{y_2-y_1}{x_2-x_1}$ ⇒ $\frac{10-7}{2-6}$

after plugging in all the values, you have $\frac{10-7}{2-6}$ .

subtract 10 - 7 as well as 2 - 6.

$\frac{10-7}{2-6}$ ⇒ $\frac{3}{-4}$

$\frac{3}{-4}$ cannot be simplified, therefore the slope of the line is $\frac{3}{-4}$ or $-\frac{3}{4}$ .

i hope this helps! have a lovely day <3

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