Solve L - 1/2 + [3/7 + (- 4/3)] * i; [- 1/2 + 3/7] + (- 4/3) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac { - 1 } { 2 } + [ \frac { 3 } { 7 } + ( \frac { - 4 } { 3 } ) ] [ \frac { - 1 } { 2 } + \frac { 3 } { 7 } ] + ( \frac { - 4 } { 3 } )$$

Evaluate

$-\frac{260}{147}\approx -1.768707483$

Solution Steps

Fraction $\frac{-1}{2}$ can be rewritten as $-\frac{1}{2}$ by extracting the negative sign.

$$-\frac{1}{2}+\left(\frac{3}{7}+\frac{-4}{3}\right)\left(\frac{-1}{2}+\frac{3}{7}\right)+\frac{-4}{3}$$

Fraction $\frac{-4}{3}$ can be rewritten as $-\frac{4}{3}$ by extracting the negative sign.

$$-\frac{1}{2}+\left(\frac{3}{7}-\frac{4}{3}\right)\left(\frac{-1}{2}+\frac{3}{7}\right)+\frac{-4}{3}$$

Least common multiple of $7$ and $3$ is $21$. Convert $\frac{3}{7}$ and $\frac{4}{3}$ to fractions with denominator $21$.

$$-\frac{1}{2}+\left(\frac{9}{21}-\frac{28}{21}\right)\left(\frac{-1}{2}+\frac{3}{7}\right)+\frac{-4}{3}$$

Since $\frac{9}{21}$ and $\frac{28}{21}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}+\frac{9-28}{21}\left(\frac{-1}{2}+\frac{3}{7}\right)+\frac{-4}{3}$$

Subtract $28$ from $9$ to get $-19$.

$$-\frac{1}{2}-\frac{19}{21}\left(\frac{-1}{2}+\frac{3}{7}\right)+\frac{-4}{3}$$

Fraction $\frac{-1}{2}$ can be rewritten as $-\frac{1}{2}$ by extracting the negative sign.

$$-\frac{1}{2}-\frac{19}{21}\left(-\frac{1}{2}+\frac{3}{7}\right)+\frac{-4}{3}$$

Least common multiple of $2$ and $7$ is $14$. Convert $-\frac{1}{2}$ and $\frac{3}{7}$ to fractions with denominator $14$.

$$-\frac{1}{2}-\frac{19}{21}\left(-\frac{7}{14}+\frac{6}{14}\right)+\frac{-4}{3}$$

Since $-\frac{7}{14}$ and $\frac{6}{14}$ have the same denominator, add them by adding their numerators.

$$-\frac{1}{2}-\frac{19}{21}\times \frac{-7+6}{14}+\frac{-4}{3}$$

Add $-7$ and $6$ to get $-1$.

$$-\frac{1}{2}-\frac{19}{21}\left(-\frac{1}{14}\right)+\frac{-4}{3}$$

Multiply $-\frac{19}{21}$ times $-\frac{1}{14}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{2}+\frac{-19\left(-1\right)}{21\times 14}+\frac{-4}{3}$$

Do the multiplications in the fraction $\frac{-19\left(-1\right)}{21\times 14}$.

$$-\frac{1}{2}+\frac{19}{294}+\frac{-4}{3}$$

Least common multiple of $2$ and $294$ is $294$. Convert $-\frac{1}{2}$ and $\frac{19}{294}$ to fractions with denominator $294$.

$$-\frac{147}{294}+\frac{19}{294}+\frac{-4}{3}$$

Since $-\frac{147}{294}$ and $\frac{19}{294}$ have the same denominator, add them by adding their numerators.

$$\frac{-147+19}{294}+\frac{-4}{3}$$

Add $-147$ and $19$ to get $-128$.

$$\frac{-128}{294}+\frac{-4}{3}$$

Reduce the fraction $\frac{-128}{294}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{64}{147}+\frac{-4}{3}$$

Fraction $\frac{-4}{3}$ can be rewritten as $-\frac{4}{3}$ by extracting the negative sign.

$$-\frac{64}{147}-\frac{4}{3}$$

Least common multiple of $147$ and $3$ is $147$. Convert $-\frac{64}{147}$ and $\frac{4}{3}$ to fractions with denominator $147$.

$$-\frac{64}{147}-\frac{196}{147}$$

Since $-\frac{64}{147}$ and $\frac{196}{147}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-64-196}{147}$$

Subtract $196$ from $-64$ to get $-260$.

$$-\frac{260}{147}$$

Factor

$-\frac{260}{147} = -1\frac{113}{147} = -1.7687074829931972$