Solve 4x-1/6=10x-7/7

$$\frac { 4 x - 1 } { 6 } = \frac { 10 x - 7 } { 7 }$$

Solve for x

$$x = \frac{35}{32} = 1\frac{3}{32} = 1.09375$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 42, the least common multiple of 6,7.

$$7\left(4x-1\right)=6\left(10x-7\right)$$

Use the distributive property to multiply 7 by 4x-1.

$$28x-7=6\left(10x-7\right)$$

Use the distributive property to multiply 6 by 10x-7.

$$28x-7=60x-42$$

Subtract 60x from both sides.

$$28x-7-60x=-42$$

Combine 28x and -60x to get -32x.

$$-32x-7=-42$$

Add 7 to both sides.

$$-32x=-42+7$$

Add -42 and 7 to get -35.

$$-32x=-35$$

Divide both sides by -32.

$$x=\frac{-35}{-32}$$

Fraction \frac{-35}{-32} can be simplified to \frac{35}{32} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{35}{32}$$