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3 years ago

-8(8 - x) = 4/5(x + 10)

Mathematics

1 answer:

Vedmedyk [2.9K]3 years ago

7 0

Answer:

x = 10

Step-by-step explanation:

Solve for x:

-8 (8 - x) = (4 (x + 10))/5

Multiply both sides by 5:

-8×5 (8 - x) = (5×4 (x + 10))/5

(5×4 (x + 10))/5 = 5/5×4 (x + 10) = 4 (x + 10):

-8×5 (8 - x) = 4 (x + 10)

5 (-8) = -40:

-40 (8 - x) = 4 (x + 10)

Expand out terms of the left hand side:

40 x - 320 = 4 (x + 10)

Expand out terms of the right hand side:

40 x - 320 = 4 x + 40

Subtract 4 x from both sides:

(40 x - 4 x) - 320 = (4 x - 4 x) + 40

40 x - 4 x = 36 x:

36 x - 320 = (4 x - 4 x) + 40

4 x - 4 x = 0:

36 x - 320 = 40

Add 320 to both sides:

36 x + (320 - 320) = 320 + 40

320 - 320 = 0:

36 x = 40 + 320

40 + 320 = 360:

36 x = 360

Divide both sides of 36 x = 360 by 36:

(36 x)/36 = 360/36

36/36 = 1:

x = 360/36

The gcd of 360 and 36 is 36, so 360/36 = (36×10)/(36×1) = 36/36×10 = 10:

Answer: x = 10

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