Solve 4(2x-1)/3-7x+1/24=3(5x-1)/8+x

$$\frac { 4 ( 2 x - 1 ) } { 3 } - \frac { 7 x + 1 } { 24 } = \frac { 3 ( 5 x - 1 ) } { 8 } + x$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 3,24,8.

$$8\times 4\left(2x-1\right)-\left(7x+1\right)=3\times 3\left(5x-1\right)+24x$$

Multiply 8 and 4 to get 32.

$$32\left(2x-1\right)-\left(7x+1\right)=3\times 3\left(5x-1\right)+24x$$

Use the distributive property to multiply 32 by 2x-1.

$$64x-32-\left(7x+1\right)=3\times 3\left(5x-1\right)+24x$$

To find the opposite of 7x+1, find the opposite of each term.

$$64x-32-7x-1=3\times 3\left(5x-1\right)+24x$$

Combine 64x and -7x to get 57x.

$$57x-32-1=3\times 3\left(5x-1\right)+24x$$

Subtract 1 from -32 to get -33.

$$57x-33=3\times 3\left(5x-1\right)+24x$$

Multiply 3 and 3 to get 9.

$$57x-33=9\left(5x-1\right)+24x$$

Use the distributive property to multiply 9 by 5x-1.

$$57x-33=45x-9+24x$$

Combine 45x and 24x to get 69x.

$$57x-33=69x-9$$

Subtract 69x from both sides.

$$57x-33-69x=-9$$

Combine 57x and -69x to get -12x.

$$-12x-33=-9$$

Add 33 to both sides.

$$-12x=-9+33$$

Add -9 and 33 to get 24.

$$-12x=24$$

Divide both sides by -12.

$$x=\frac{24}{-12}$$

Divide 24 by -12 to get -2.

$$x=-2$$