Solve -2 3 -[ -4 5 - 1 2 ]=[ 2 3 -( -4 5 )]- 1 2 ? | 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

$$\frac{-2}{3}-[\frac{-4}{5}-\frac{1}{2}]=[\frac{2}{3}-(\frac{-4}{5})]-\frac{1}{2}?$$

Verify

$\text{false}$

Solution Steps

Fraction $\frac{-2}{3}$ can be rewritten as $-\frac{2}{3}$ by extracting the negative sign.

$$-\frac{2}{3}-\left(\frac{-4}{5}-\frac{1}{2}\right)=\frac{2}{3}-\frac{-4}{5}-\frac{1}{2}$$

Fraction $\frac{-4}{5}$ can be rewritten as $-\frac{4}{5}$ by extracting the negative sign.

$$-\frac{2}{3}-\left(-\frac{4}{5}-\frac{1}{2}\right)=\frac{2}{3}-\frac{-4}{5}-\frac{1}{2}$$

Least common multiple of $5$ and $2$ is $10$. Convert $-\frac{4}{5}$ and $\frac{1}{2}$ to fractions with denominator $10$.

$$-\frac{2}{3}-\left(-\frac{8}{10}-\frac{5}{10}\right)=\frac{2}{3}-\frac{-4}{5}-\frac{1}{2}$$

Since $-\frac{8}{10}$ and $\frac{5}{10}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}-\frac{-8-5}{10}=\frac{2}{3}-\frac{-4}{5}-\frac{1}{2}$$

Subtract $5$ from $-8$ to get $-13$.

$$-\frac{2}{3}-\left(-\frac{13}{10}\right)=\frac{2}{3}-\frac{-4}{5}-\frac{1}{2}$$

The opposite of $-\frac{13}{10}$ is $\frac{13}{10}$.

$$-\frac{2}{3}+\frac{13}{10}=\frac{2}{3}-\frac{-4}{5}-\frac{1}{2}$$

Least common multiple of $3$ and $10$ is $30$. Convert $-\frac{2}{3}$ and $\frac{13}{10}$ to fractions with denominator $30$.

$$-\frac{20}{30}+\frac{39}{30}=\frac{2}{3}-\frac{-4}{5}-\frac{1}{2}$$

Since $-\frac{20}{30}$ and $\frac{39}{30}$ have the same denominator, add them by adding their numerators.

$$\frac{-20+39}{30}=\frac{2}{3}-\frac{-4}{5}-\frac{1}{2}$$

Add $-20$ and $39$ to get $19$.

$$\frac{19}{30}=\frac{2}{3}-\frac{-4}{5}-\frac{1}{2}$$

Fraction $\frac{-4}{5}$ can be rewritten as $-\frac{4}{5}$ by extracting the negative sign.

$$\frac{19}{30}=\frac{2}{3}-\left(-\frac{4}{5}\right)-\frac{1}{2}$$

The opposite of $-\frac{4}{5}$ is $\frac{4}{5}$.

$$\frac{19}{30}=\frac{2}{3}+\frac{4}{5}-\frac{1}{2}$$

Least common multiple of $3$ and $5$ is $15$. Convert $\frac{2}{3}$ and $\frac{4}{5}$ to fractions with denominator $15$.

$$\frac{19}{30}=\frac{10}{15}+\frac{12}{15}-\frac{1}{2}$$

Since $\frac{10}{15}$ and $\frac{12}{15}$ have the same denominator, add them by adding their numerators.

$$\frac{19}{30}=\frac{10+12}{15}-\frac{1}{2}$$

Add $10$ and $12$ to get $22$.

$$\frac{19}{30}=\frac{22}{15}-\frac{1}{2}$$

Least common multiple of $15$ and $2$ is $30$. Convert $\frac{22}{15}$ and $\frac{1}{2}$ to fractions with denominator $30$.

$$\frac{19}{30}=\frac{44}{30}-\frac{15}{30}$$

Since $\frac{44}{30}$ and $\frac{15}{30}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{19}{30}=\frac{44-15}{30}$$

Subtract $15$ from $44$ to get $29$.

$$\frac{19}{30}=\frac{29}{30}$$

Compare $\frac{19}{30}$ and $\frac{29}{30}$.

$$\text{false}$$