Solve x + [6/7 + (- 8/11)] = (- 1/2 + 6/7) + (- 8/11) | 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

$$x+[\frac{6}{7}+(\frac{-8}{11})]=(\frac{-1}{2}+\frac{6}{7})+(\frac{-8}{11})$$

Solve for x

$x=-\frac{1}{2}=-0.5$

Steps for Solving Linear Equation

Fraction $\frac{-8}{11}$ can be rewritten as $-\frac{8}{11}$ by extracting the negative sign.

$$x+\frac{6}{7}-\frac{8}{11}=\frac{-1}{2}+\frac{6}{7}+\frac{-8}{11}$$

Least common multiple of $7$ and $11$ is $77$. Convert $\frac{6}{7}$ and $\frac{8}{11}$ to fractions with denominator $77$.

$$x+\frac{66}{77}-\frac{56}{77}=\frac{-1}{2}+\frac{6}{7}+\frac{-8}{11}$$

Since $\frac{66}{77}$ and $\frac{56}{77}$ have the same denominator, subtract them by subtracting their numerators.

$$x+\frac{66-56}{77}=\frac{-1}{2}+\frac{6}{7}+\frac{-8}{11}$$

Subtract $56$ from $66$ to get $10$.

$$x+\frac{10}{77}=\frac{-1}{2}+\frac{6}{7}+\frac{-8}{11}$$

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

$$x+\frac{10}{77}=-\frac{1}{2}+\frac{6}{7}+\frac{-8}{11}$$

Least common multiple of $2$ and $7$ is $14$. Convert $-\frac{1}{2}$ and $\frac{6}{7}$ to fractions with denominator $14$.

$$x+\frac{10}{77}=-\frac{7}{14}+\frac{12}{14}+\frac{-8}{11}$$

Since $-\frac{7}{14}$ and $\frac{12}{14}$ have the same denominator, add them by adding their numerators.

$$x+\frac{10}{77}=\frac{-7+12}{14}+\frac{-8}{11}$$

Add $-7$ and $12$ to get $5$.

$$x+\frac{10}{77}=\frac{5}{14}+\frac{-8}{11}$$

Fraction $\frac{-8}{11}$ can be rewritten as $-\frac{8}{11}$ by extracting the negative sign.

$$x+\frac{10}{77}=\frac{5}{14}-\frac{8}{11}$$

Least common multiple of $14$ and $11$ is $154$. Convert $\frac{5}{14}$ and $\frac{8}{11}$ to fractions with denominator $154$.

$$x+\frac{10}{77}=\frac{55}{154}-\frac{112}{154}$$

Since $\frac{55}{154}$ and $\frac{112}{154}$ have the same denominator, subtract them by subtracting their numerators.

$$x+\frac{10}{77}=\frac{55-112}{154}$$

Subtract $112$ from $55$ to get $-57$.

$$x+\frac{10}{77}=-\frac{57}{154}$$

Subtract $\frac{10}{77}$ from both sides.

$$x=-\frac{57}{154}-\frac{10}{77}$$

Least common multiple of $154$ and $77$ is $154$. Convert $-\frac{57}{154}$ and $\frac{10}{77}$ to fractions with denominator $154$.

$$x=-\frac{57}{154}-\frac{20}{154}$$

Since $-\frac{57}{154}$ and $\frac{20}{154}$ have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{-57-20}{154}$$

Subtract $20$ from $-57$ to get $-77$.

$$x=\frac{-77}{154}$$

Reduce the fraction $\frac{-77}{154}$ to lowest terms by extracting and canceling out $77$.

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