Solve 9-(3/2+1)*9+12*2/2+6=101/2

$$9 - ( \frac { 3 } { 2 } + 1 ) \times 9 + 12 \times \frac { 2 } { 2 } + 6 = 10 \frac { 1 } { 2 }$$

Verify

Solution Steps

Multiply both sides of the equation by 2.

$$2\left(9-\left(\frac{3}{2}+1\right)\times 9\right)+12\times 2+12=10\times 2+1$$

Convert 1 to fraction \frac{2}{2}.

$$2\left(9-\left(\frac{3}{2}+\frac{2}{2}\right)\times 9\right)+12\times 2+12=10\times 2+1$$

Since \frac{3}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$2\left(9-\frac{3+2}{2}\times 9\right)+12\times 2+12=10\times 2+1$$

Add 3 and 2 to get 5.

$$2\left(9-\frac{5}{2}\times 9\right)+12\times 2+12=10\times 2+1$$

Express \frac{5}{2}\times 9 as a single fraction.

$$2\left(9-\frac{5\times 9}{2}\right)+12\times 2+12=10\times 2+1$$

Multiply 5 and 9 to get 45.

$$2\left(9-\frac{45}{2}\right)+12\times 2+12=10\times 2+1$$

Convert 9 to fraction \frac{18}{2}.

$$2\left(\frac{18}{2}-\frac{45}{2}\right)+12\times 2+12=10\times 2+1$$

Since \frac{18}{2} and \frac{45}{2} have the same denominator, subtract them by subtracting their numerators.

$$2\times \frac{18-45}{2}+12\times 2+12=10\times 2+1$$

Subtract 45 from 18 to get -27.

$$2\left(-\frac{27}{2}\right)+12\times 2+12=10\times 2+1$$

Cancel out 2 and 2.

$$-27+12\times 2+12=10\times 2+1$$

Multiply 12 and 2 to get 24.

$$-27+24+12=10\times 2+1$$

Add -27 and 24 to get -3.

$$-3+12=10\times 2+1$$

Add -3 and 12 to get 9.

$$9=10\times 2+1$$

Multiply 10 and 2 to get 20.

$$9=20+1$$

Add 20 and 1 to get 21.

$$9=21$$

Compare 9 and 21.

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