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3 years ago

3/4x-5/6=2/3x how to solve?

Mathematics

1 answer:

Ronch [10]3 years ago

4 0

Answer:

The answer is 10.

Step-by-step explanation:

Multiply both sides of the equation by 12.

12( 3/4x - 5/6) = 12 times 2/3x.

Distribute 12 through the parenthesis.

12 times 3/4x - 12 times 5/6 = 12 times 2/3x.

Reduce the numbers with greatest common divisor 3.

12 times 3/4x - 12 times 5/6 = 4 times 2x.

Reduce the numbers with greatest common divisor 4.

3 times 3x - 12 times 5/6 = 4 times 2x.

Reduce the numbers with greatest common divisor 6.

3 times 3x - 2 times 5 = 4 times 2x.

Calculate the product, 4 times 2x.

3 times 3x - 2 times 5 = 8x.

Calculate the product 3 times 3x.

9x - 2 times 5 = 8x.

Multiply the numbers - 2 times 5.

9x -10 = 8x.

Move the constant to the right by adding its opposite to both sides.

9x - 10 + 10 = 8x + 10.

Eliminate the opposites, -10 + 10.

9x = 8x + 10.

Move the variable to the left by adding its opposite to both sides.

9x -8x = 8x -8x + 10.

Now eliminate the opposites

9x - 8x = 10.

Collect the like terms by subtracting their coefficients.

(9-8)x

Subtract the numbers.

1x.

When the term has a coefficient of 1, it doesn't have to be written, so it's basically x.

Then, x will equal to 10!

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3 years ago

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What point in the feasible region maximizes the objective function, 3x + y ≤ 12, x+y ≤5, x ≥0,y ≥0

forsale [732]

Step-by-step explanation:

We have to find the point in the feasible region which maximizes the objective function. To find that point first we need to graph the given inequalities to find the feasible region.

Steps to graph 3x + y ≤ 12:

First we graph 3x + y = 12 then shade the graph for ≤.

plug any value of x say x=0 and x=2 into 3x + y = 12 to find points.

plug x=0

3x + y = 12

3(0) + y = 12

0 + y = 12

y = 12

Hence first point is (0,12)

Similarly plugging x=2 will give y=6

Hence second point is (2,6)

Now graph both points and joint them by a straight line.

test for shading.

plug any test point which is not on the graph of line like (0,0) into original inequality 3x + y ≤ 12:

3(0) + (0) ≤ 12

0 + 0 ≤ 12

0 ≤ 12

Which is true so shading will be in the direction of test point (0,0)

We can repeat same procedure to graph other inequalities.

From graph we see that ABCD is feasible region whose corner points will result into maximum or minimu for objective function.

Since objective function is not given in the question so i will explain the process.

To find the maximum value of objective function we plug each corner point of feasible region into objective function. Whichever point gives maximum value will be the answer

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3 years ago