Solve equation for 5x-14=8x+4

Mathematics

2 answers:

creativ13 [48]3 years ago

6 0

My answer-

Simplifying 5x + -14 = 8x + 4

Reorder the terms: -14 + 5x = 8x + 4 Reorder the terms: -14 + 5x = 4 + 8x

Solving -14 + 5x = 4 + 8x Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right. Add '-8x' to each side of the equation. -14 + 5x + -8x = 4 + 8x + -8x

Combine like terms: 5x + -8x = -3x -14 + -3x = 4 + 8x + -8x

Combine like terms: 8x + -8x = 0 -14 + -3x = 4 + 0 -14 + -3x = 4 Add '14' to

each side of the equation. -14 + 14 + -3x = 4 + 14

Combine like terms: -14 + 14 = 0 0 + -3x = 4 + 14 -3x = 4 + 14

Combine like terms: 4 + 14 = 18 -3x = 18 <span>

Divide each side by '-3'. x = -6

Simplifying x = -6

If you need anything else on brainly let me know :)</span>

IgorC [24]3 years ago

6 0

Remember, you can do anything to an equation as long as you do it to both sides

get 1 of the x on one side

5x-14=8x+4
minus 5x both sides (we want on left side because 8>5 and I like positive stuff)

5x-5x-14=8x-5x+4
0-14=3x+4
-14=3x+4
minus 4 both sides
-14-4=3x+4-4
-18=3x+0
-18=3x
divide both sides by 3
remember, negative/positive=negative
-18/3=(3x)/3
-6=x(3/3)
-6=x(1)
-6=x
x=-6

You might be interested in

[Will mark as brainliest]

Aleks04 [339]

The answer is: $f^{-1} = 4x^2-3,\quad\text{for } x \leq 0$

The inverse of a function $f(x)$ is another function, $f^{-1}(x)$ , with the following property:

$f(f^{-1}(x)) = f^{-1}(f(x)) = x$

In other words, the inverse of a function does exactly "the opposite" of what the original function does, and so if you compute them both in sequence you return to the starting point.

Think for example to a function that doubles the input, $f(x)=2x$ , and one that halves it: $f(x)= \frac{x}{2}$ . Their composition is clearly the identity function $f(x)=x$ , since you consider "twice the half of something", or "half the double of something".

In general, to invert a function $y=f(x)$ , you have to solve the expression for $x$ , writing an expression like $x = g(y)$ . If you manage to do so, then $g$ is the inverse of $f$ .

In your case, you have

$f(x) = y = -\frac{1}{2}\sqrt{x+3}$

Multiply both sides by $-2$ to get

$-2y = \sqrt{x+3}$

Square both sides to get

$4y^2 = x+3$

Finally, subtract 3 from both sides to get

$x = 4y^2 - 3$

Since the name of the variables doesn't really have a meaning, you can say that the inverse function is

$f^{-1}(x) = 4x^2 - 3$

As for the domain of the inverse function, remember what we said ad the beginning: if the original function goes from set A (domain) to set B (codomain), then the inverse function goes from set B (domain) to set A (codomain). This means that the inverse function is defined on an element in B if and only if that element belongs to the range of the original function, i.e. the set of the elements of the codomain $b \in B$ such that there exists $a \in A : f(a)=b$ . So, we need the range of $f(x)$ .

We know that the range of $g(x)=\sqrt{x}$ is $[0,\infty)$ . When you transform it to $g(x)=\sqrt{x+3}$ you simply translate the graph horizontally, so the range doesn't change. But when you multiply the function times $-\frac{1}{2}$ you affect both extrema of the range, turning it into $(-\infty,0]$ , which you can simply write as $x \leq 0$