Solve [2-(1-0.5x2/3)]*[7+(-1)^3]

$$[ 2 - ( 1 - 0.5 x \frac { 2 } { 3 } ) ] \times [ 7 + ( - 1 ) ^ { 3 } ]$$

Evaluate

$$2\left(x+3\right)$$

Solution Steps

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\left(2-\left(1-\frac{1}{2}x\times \frac{2}{3}\right)\right)\left(7+\left(-1\right)^{3}\right)$$

Multiply \frac{1}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\left(2-\left(1-\frac{1\times 2}{2\times 3}x\right)\right)\left(7+\left(-1\right)^{3}\right)$$

Cancel out 2 in both numerator and denominator.

$$\left(2-\left(1-\frac{1}{3}x\right)\right)\left(7+\left(-1\right)^{3}\right)$$

To find the opposite of 1-\frac{1}{3}x, find the opposite of each term.

$$\left(2-1-\left(-\frac{1}{3}x\right)\right)\left(7+\left(-1\right)^{3}\right)$$

The opposite of -\frac{1}{3}x is \frac{1}{3}x.

$$\left(2-1+\frac{1}{3}x\right)\left(7+\left(-1\right)^{3}\right)$$

Subtract 1 from 2 to get 1.

$$\left(1+\frac{1}{3}x\right)\left(7+\left(-1\right)^{3}\right)$$

Calculate -1 to the power of 3 and get -1.

$$\left(1+\frac{1}{3}x\right)\left(7-1\right)$$

Subtract 1 from 7 to get 6.

$$\left(1+\frac{1}{3}x\right)\times 6$$

Use the distributive property to multiply 1+\frac{1}{3}x by 6.

$$6+\frac{1}{3}x\times 6$$

Multiply \frac{1}{3} and 6 to get \frac{6}{3}.

$$6+\frac{6}{3}x$$

Divide 6 by 3 to get 2.

$$6+2x$$

Expand

$$2x+6$$

Solution Steps

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\left(2-\left(1-\frac{1}{2}x\times \frac{2}{3}\right)\right)\left(7+\left(-1\right)^{3}\right)$$

Multiply \frac{1}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\left(2-\left(1-\frac{1\times 2}{2\times 3}x\right)\right)\left(7+\left(-1\right)^{3}\right)$$

Cancel out 2 in both numerator and denominator.

$$\left(2-\left(1-\frac{1}{3}x\right)\right)\left(7+\left(-1\right)^{3}\right)$$

To find the opposite of 1-\frac{1}{3}x, find the opposite of each term.

$$\left(2-1-\left(-\frac{1}{3}x\right)\right)\left(7+\left(-1\right)^{3}\right)$$

The opposite of -\frac{1}{3}x is \frac{1}{3}x.

$$\left(2-1+\frac{1}{3}x\right)\left(7+\left(-1\right)^{3}\right)$$

Subtract 1 from 2 to get 1.

$$\left(1+\frac{1}{3}x\right)\left(7+\left(-1\right)^{3}\right)$$

Calculate -1 to the power of 3 and get -1.

$$\left(1+\frac{1}{3}x\right)\left(7-1\right)$$

Subtract 1 from 7 to get 6.

$$\left(1+\frac{1}{3}x\right)\times 6$$

Use the distributive property to multiply 1+\frac{1}{3}x by 6.

$$6+\frac{1}{3}x\times 6$$

Multiply \frac{1}{3} and 6 to get \frac{6}{3}.

$$6+\frac{6}{3}x$$

Divide 6 by 3 to get 2.

$$6+2x$$