Solve 7-4*[5-{(-3/2)^2-(7/4-3/2)}]

$$7 - 4 \times [ 5 - \{ ( - \frac { 3 } { 2 } ) ^ { 2 } - ( \frac { 7 } { 4 } - \frac { 3 } { 2 } ) \} ]$$

Evaluate

$$-5$$

Solution Steps

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$7-4\left(5-\left(\frac{9}{4}-\left(\frac{7}{4}-\frac{3}{2}\right)\right)\right)$$

Least common multiple of 4 and 2 is 4. Convert \frac{7}{4} and \frac{3}{2} to fractions with denominator 4.

$$7-4\left(5-\left(\frac{9}{4}-\left(\frac{7}{4}-\frac{6}{4}\right)\right)\right)$$

Since \frac{7}{4} and \frac{6}{4} have the same denominator, subtract them by subtracting their numerators.

$$7-4\left(5-\left(\frac{9}{4}-\frac{7-6}{4}\right)\right)$$

Subtract 6 from 7 to get 1.

$$7-4\left(5-\left(\frac{9}{4}-\frac{1}{4}\right)\right)$$

Since \frac{9}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$7-4\left(5-\frac{9-1}{4}\right)$$

Subtract 1 from 9 to get 8.

$$7-4\left(5-\frac{8}{4}\right)$$

Divide 8 by 4 to get 2.

$$7-4\left(5-2\right)$$

Subtract 2 from 5 to get 3.

$$7-4\times 3$$

Multiply 4 and 3 to get 12.

$$7-12$$

Subtract 12 from 7 to get -5.

$$-5$$

Factor

$$-5$$