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

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

Solve for x

$$x=-\frac{44}{59}\approx -0.745762712$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 105, the least common multiple of 7,5,3.

$$15\left(3x+2\right)+21\times 4\left(x+1\right)=35\times 2\left(x+1\right)$$

Use the distributive property to multiply 15 by 3x+2.

$$45x+30+21\times 4\left(x+1\right)=35\times 2\left(x+1\right)$$

Multiply 21 and 4 to get 84.

$$45x+30+84\left(x+1\right)=35\times 2\left(x+1\right)$$

Use the distributive property to multiply 84 by x+1.

$$45x+30+84x+84=35\times 2\left(x+1\right)$$

Combine 45x and 84x to get 129x.

$$129x+30+84=35\times 2\left(x+1\right)$$

Add 30 and 84 to get 114.

$$129x+114=35\times 2\left(x+1\right)$$

Multiply 35 and 2 to get 70.

$$129x+114=70\left(x+1\right)$$

Use the distributive property to multiply 70 by x+1.

$$129x+114=70x+70$$

Subtract 70x from both sides.

$$129x+114-70x=70$$

Combine 129x and -70x to get 59x.

$$59x+114=70$$

Subtract 114 from both sides.

$$59x=70-114$$

Subtract 114 from 70 to get -44.

$$59x=-44$$

Divide both sides by 59.

$$x=\frac{-44}{59}$$

Fraction \frac{-44}{59} can be rewritten as -\frac{44}{59} by extracting the negative sign.

$$x=-\frac{44}{59}$$