Question

Solve the equation and check your solution. (If an answer does not exist enter DNE. If all real numbers are solutions and to REALS.)

2x/5 + 5x = 16/15

Answer 1

2x/5 + 5x = 16/15

6x + 75x = 16

81x = 16

x = 16/81

Checking this solution:

(2/5)(16/81) + 5(16/81) = 16/15

32/405 + 80/81 = 16/15

32/405 + 400/405 = 432/405

The solution is correct.

Answer 2

To solve the equation 2x/5 + 5x = 16/15, we first combine like terms and eliminate the fraction. By simplifying and isolating x, we find that x = 16/81. To check our solution, we substitute it back into the equation and verify that both sides are equal.

Step-by-step explanation:

To solve the equation, we can start by combining like terms on the left side:

2x/5 + 5x = 16/15

Multiplying both sides by 5 to eliminate the fraction, we get:

2x + 25x = 16/15 * 5

27x = 80/15

Next, we can simplify the right side of the equation:

27x = 16/3

To isolate x, we divide both sides of the equation by 27:

x = 16/3 ÷ 27

Now we can evaluate x:

x = 16/3 * 1/27

By multiplying the numerators and denominators, we get:

x = 16 ÷ 81

So, the solution to the equation is x = 16/81.

To check our solution, we substitute x = 16/81 back into the original equation:

2(16/81)/5 + 5(16/81) = 16/15

Simplifying both sides of the equation:

32/405 + 80/81 = 16/15

After finding a common denominator, we have:

32/405 + 400/405 = 16/15

Combining the fractions:

432/405 = 16/15

Both sides of the equation are equal, so the solution x = 16/81 is correct.