What is -3/2 (-6+2\div (1-1/2)) ?

The solution to -3/2 (-6+2\div (1-1/2)) is 3

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-3/2 (-6+2\div (1-1/2))

- \frac{3}{2} (- 6 + 2 \div (1 - \frac{1}{2}))

3

Solution steps

- \frac{3}{2} (- 6 + 2 \div (1 - \frac{1}{2}))

Follow the PEMDAS order of operations

Calculate within parentheses

(- 6 + 2 \div (1 - \frac{1}{2})) : - 2

- 6 + 2 \div (1 - \frac{1}{2})

Calculate within parentheses

(1 - \frac{1}{2}) : \frac{1}{2}

1 - \frac{1}{2}

1 - \frac{1}{2} = \frac{1}{2}

1 - \frac{1}{2}

Convert element to fraction:

1 = \frac{1 \cdot 2}{2}

= \frac{1 \cdot 2}{2} - \frac{1}{2}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{1 \cdot 2 - 1}{2}

1 \cdot 2 - 1 = 1

1 \cdot 2 - 1

Multiply the numbers:

1 \cdot 2 = 2

= 2 - 1

Subtract the numbers:

2 - 1 = 1

= 1

= \frac{1}{2}

= \frac{1}{2}

= - 6 + 2 \div \frac{1}{2}

Multiply and divide (left to right)

2 \div \frac{1}{2} : 4

2 \div \frac{1}{2}

Convert element to fraction:

2 = \frac{2}{1}

= \frac{2}{1} \div \frac{1}{2}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{2}{1} \cdot \frac{2}{1}

Apply rule

\frac{a}{1} = a

= 2 \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 4

= - 6 + 4

Add and subtract (left to right)

- 6 + 4 : - 2

- 6 + 4

- 6 + 4 = - 2

= - 2

= - 2

= - \frac{3}{2} (- 2)

Multiply and divide (left to right)

- \frac{3}{2} (- 2) : 3

- \frac{3}{2} (- 2)

Apply rule

- a \cdot (- b) = a \cdot b

- \frac{3}{2} (- 2) = \frac{3}{2} \cdot 2

Convert element to fraction:

2 = \frac{2}{1}

= \frac{3}{2} \cdot \frac{2}{1}

Cross-cancel common factor:

2

= \frac{3}{1}

Divide the numbers:

\frac{3}{1} = 3

= 3

= 3

2 (3)^{2} + (4 - 3)^{2}

\frac{1}{3} (- 1) - \frac{7}{8}

16 + 34 \div 17 - 7 \times 2

- 5 (- 2)^{3} - 3 (- 2)^{2} - 9 (- 2) + 2

(- 2) - (- 3) - (- 20) - (30)