Solve 11x+5/6x-7=1-2/7

$$\frac { 11 x + 5 } { 6 x - 7 } = 1 - \frac { 2 } { 7 }$$

Solve for x

$$x = -\frac{70}{47} = -1\frac{23}{47} \approx -1.489361702$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{7}{6} since division by zero is not defined. Multiply both sides of the equation by 7\left(6x-7\right), the least common multiple of 6x-7,7.

$$7\left(11x+5\right)=7\left(6x-7\right)+7\left(6x-7\right)\left(-\frac{2}{7}\right)$$

Use the distributive property to multiply 7 by 11x+5.

$$77x+35=7\left(6x-7\right)+7\left(6x-7\right)\left(-\frac{2}{7}\right)$$

Use the distributive property to multiply 7 by 6x-7.

$$77x+35=42x-49+7\left(6x-7\right)\left(-\frac{2}{7}\right)$$

Multiply 7 and -\frac{2}{7} to get -2.

$$77x+35=42x-49-2\left(6x-7\right)$$

Use the distributive property to multiply -2 by 6x-7.

$$77x+35=42x-49-12x+14$$

Combine 42x and -12x to get 30x.

$$77x+35=30x-49+14$$

Add -49 and 14 to get -35.

$$77x+35=30x-35$$

Subtract 30x from both sides.

$$77x+35-30x=-35$$

Combine 77x and -30x to get 47x.

$$47x+35=-35$$

Subtract 35 from both sides.

$$47x=-35-35$$

Subtract 35 from -35 to get -70.

$$47x=-70$$

Divide both sides by 47.

$$x=\frac{-70}{47}$$

Fraction \frac{-70}{47} can be rewritten as -\frac{70}{47} by extracting the negative sign.

$$x=-\frac{70}{47}$$