Question

1/3(2x-4) -1/5 (2x-1)=1/15(4x-17)

Answer 1

Відповідь:13(2x−4)+−15(2x−1)=115(4x−17)13(2−4)+−15(2−1)=115(4−17)

Покрокове пояснення:

Answer 2

To solve the equation 1/3(2x-4) - 1/5(2x-1) = 1/15(4x-17), we'll begin by simplifying the equation step by step:

1/3(2x-4) - 1/5(2x-1) = 1/15(4x-17)

Multiply each term by the respective denominator to eliminate the fractions:

(1/3)(2x-4) - (1/5)(2x-1) = (1/15)(4x-17)

Multiply 1/3 by (2x-4):

(2/3)x - 4/3 - (1/5)(2x-1) = (1/15)(4x-17)

Multiply 1/5 by (2x-1):

(2/3)x - 4/3 - (2/5)x + 1/5 = (1/15)(4x-17)

Now we can simplify the equation further:

(2/3)x - (2/5)x - 4/3 + 1/5 = (1/15)(4x-17)

To combine like terms, we need a common denominator:

[(10/15)x - (6/15)x] - (20/15) + (3/15) = (1/15)(4x-17)

Simplifying:

(4/15)x - (17/15) = (1/15)(4x-17)

Next, we can eliminate the fractions by multiplying every term by 15:

15[(4/15)x - (17/15)] = 15[(1/15)(4x-17)]

This simplifies to:

4x - 17 = 4x - 17

At this point, we can observe that both sides of the equation are identical. This implies that the equation is an identity, meaning it holds true for all values of x. Therefore, the solution is x ∈ ℝ (real numbers).