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3 years ago

7x+1/2(x+1/4)=3(6x-9)-8

Mathematics

1 answer:

ycow [4]3 years ago

5 0

Answer:

x = 381/24 = 3 29/84

Step-by-step explanation:

7x + 1/2(x + 1/4) = 3(6x - 9) - 8

Use the distributive property to multiply 1/2 by x + 1/4.

7x + 1/2x + 1/8 = 3(6x - 9) - 8

Combine 7x (14/2x) and 1/2x to get 15/2.

15/2x + 1/8 = 3(6x - 9) - 8

Use the distributive property to multiply 3 by 6x - 9.

15/2x + 1/8 = 18x - 27 - 8

Subtract 8 from -27 to get -35.

15/2x + 1/8 = 18x - 35

Subtract 18x from both sides.

-21/2x + 1/8 = -35

Subtract 1/8 from both sides.

-21/2x = -35 - 1/8

-35 is the same as -280/8.

-21/2x = (-280 - 1)/8

Subtract 1 from -280 to get -281.

-21/2x = -281/8

Multiply both sides by -2/21 (reciprocal of -21/2).

x = (-281 * -2)/(8 * 21)

You can cross cancel -2 and 8 by extracting 2 (they become -1 and 4 respectively).

x = (-281 * -1)/(4 * 21)

Multiply -281 by -1 to get 281.

x = 281/(4 * 21)

Multiply 4 by 21 to get 84.

x = 281/84

Can this fraction be simplified into a mixed number? Yes it can. It becomes 3 29/84. (252 (3 * 84) + 29 = 281)

x = 3 29/84

Work check: x is substituted for 281/84 (convenience)

7 * 281/84 + 1/2(281/84 + 1/4) = 3((6 * 281)/84 - 9) - 8

1967/84 + 1/2(281/84 + 1/4) = 3((6 * 281)/84 - 9) - 8

1967/84 + 1/2(302/84) = 3((6 * 281)/84 - 9) - 8

(1967 + 151)/84 = 3((6 * 281)/84 - 9) - 8

2118/84 = 3(1686/84 - 9) - 8

2118/84 = 3((1686 - 756)/84) - 8

2118/84 = 3(930/84) - 8

2118/84 = 2790/84 - 672/84

2118/84 = (2790 - 672)/84

2118/84 = 2118/84

So x = 3 29/84 is correct.

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