Question

0,4(x-7)+0,2(2x-9), 4/5x-1/10x+1/2x=2 2/3​

Answer 1

0.4 * (x - 7) + 0.2 * (2x - 9) = 0.4x - 2.8 + 0.4x - 1.8 = 0.8x - 4.6

4/5x - 1/10x + 1/2x = 2 2/3

6/5x = 2 2/3

x = 8/3 * 5/6

x = 20/9

x = 2 2/9

Answer 2

To solve the equation 0.4(x-7) + 0.2(2x-9) + (4/5)x - (1/10)x + (1/2)x = 2 2/3, we need to simplify and combine like terms.

Step 1: Distribute the coefficients 0.4(x-7) = 0.4x - 2.8 0.2(2x-9) = 0.4x - 1.8

Step 2: Combine like terms (0.4x - 2.8) + (0.4x - 1.8) + (4/5)x - (1/10)x + (1/2)x = 2 2/3

Now, let's combine the x terms: 0.4x + 0.4x + (4/5)x - (1/10)x + (1/2)x = 2 2/3

To combine the fractions, we need to find a common denominator for (4/5) and (1/10). The common denominator is 10.

(4/5) = (8/10), so the equation becomes: 0.4x + 0.4x + (8/10)x - (1/10)x + (1/2)x = 2 2/3

Now, all the x terms have the same denominator, so we can combine them: (0.4 + 0.4 + 8/10 - 1/10 + 1/2)x = 2 2/3

(1.2 + 7/10)x = 2 2/3

Step 3: Convert 2 2/3 to a fraction 2 2/3 = (2 * 3 + 2)/3 = 8/3

Now, the equation becomes: (1.2 + 7/10)x = 8/3

Step 4: Simplify and solve for x To solve for x, we need to get rid of the coefficients on the left side of the equation. Let's first combine the decimal and fraction:

1.2 + 7/10 = (12/10 + 7/10) = 19/10

Now the equation becomes: (19/10)x = 8/3

To isolate x, we can divide both sides of the equation by (19/10):

x = (8/3) ÷ (19/10)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

x = (8/3) * (10/19)

x = (80/57) or approximately 1.4035 (rounded to four decimal places).

So, the solution to the equation is x = 80/57 or approximately 1.4035.