Ask question

Ask question

All categories

3 years ago

10

What is the solution to the linear equation? 2/3x - 1/2=1/3 + 5/6x

1 answer:

Alexxx [7]3 years ago

7 0

Answer:

The answer is x = -5

Step-by-step explanation:

2/3x - 1/2 = 1/3 + 5/6. First, multiply the entire equation by the common denominator of 6. This will get rid of the fractions. :)

6(2/3x - 1/2) = 6(1/3 + 5/6x)

4x - 3 = 2 + 5x subtract 5x from both sides

4x - 5x - 3 = 2 add 3 to both sides

4x - 5x = 2 + 3 combine terms

-x = 5 multiply by -1 to make x positive

You might be interested in

Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)

Lisa [10]

Answer:

$f(x) = 4x^2 - 3x + 6$

Step-by-step explanation:

Quadratic function is given as $f(x) = ax^2 + bx + c$

Let's find a, b and c:

Substituting (0, 6):

$6 = a(0)^2 + b(0) + c$

$6 = 0 + 0 + c$

$c = 6$

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

$f(x) = ax^2 + bx + c$

$16 = a(2)^2 + b(2) + 6$

$16 = 4a + 2b + 6$

$16 - 6 = 4a + 2b + 6 - 6$

$10 = 4a + 2b$

$10 = 2(2a + b)$

$\frac{10}{2} = \frac{2(2a + b)}{2}$

$5 = 2a + b$

$2a + b = 5$ => (Equation 1)

Substituting (3, 33), and c = 6

$f(x) = ax^2 + bx + x$

$33 = a(3)^2 + b(3) + 6$

$33 = 9a + 3b + 6$

$33 - 6 = 9a + 3b + 6 - 6$

$27 = 9a + 3b$

$27 = 3(3a + b)$

$\frac{27}{3} = \frac{3(3a + b)}{3}$

$9 = 3a + b$

$3a + b = 9$ => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

$3a + b = 9$

$2a + b = 5$

$a = 4$

Replace a with 4 in equation 2.

$2a + b = 5$

$2(4) + b = 5$

$8 + b = 5$

$8 + b - 8 = 5 - 8$

$b = -3$

The quadratic function that represents the given 3 points would be as follows:

$f(x) = ax^2 + bx + c$

$f(x) = (4)x^2 + (-3)x + 6$

$f(x) = 4x^2 - 3x + 6$

6 0

4 years ago

What does x is greater than 5 mean

kotegsom [21]

Answer:

That x is any number bigger that 5 so 6 plus

Step-by-step explanation:

3 0

4 years ago

An element with a mass of 320 grams decays by 5.1% per minute. To the nearest tenth of a minute, how long will it be until there

HACTEHA [7]

Answer:

X=9

Step-by-step explanation:

7 0

3 years ago

Which represents the solution(s) of the system of equations, y = -x2 + 6x + 16 and y = - 4x + 37? Determine the solution set

AysviL [449]

Answer:

The answer is c

Step-by-step explanation:

(7,9) (3,25)

3 0

3 years ago

4(a + 2) = -4<br> whats A

OLga [1]

The answer is -3 because -3+2=-1 then -1(4)=-4

4 0

3 years ago

Read 2 more answers