Solve 12(x+1)+3x-5<7(x+1)

$$12 ( x + 1 ) + 3 x - 5 < 7 ( x + 1 )$$

Solve for x

$$x<0$$

Solution Steps

Use the distributive property to multiply 12 by x+1.

$$12x+12+3x-5<7\left(x+1\right)$$

Combine 12x and 3x to get 15x.

$$15x+12-5<7\left(x+1\right)$$

Subtract 5 from 12 to get 7.

$$15x+7<7\left(x+1\right)$$

Use the distributive property to multiply 7 by x+1.

$$15x+7<7x+7$$

Subtract 7x from both sides.

$$15x+7-7x<7$$

Combine 15x and -7x to get 8x.

$$8x+7<7$$

Subtract 7 from both sides.

$$8x<7-7$$

Subtract 7 from 7 to get 0.

$$8x<0$$

Product of two numbers is <0 if one is >0 and the other is <0. Since 8>0, x must be <0.

$$x<0$$