Solve 5(5x+8-4)<3(8x+7-4)+(2x+6x-9)-8(4x-7)

$$5 ( 5 x + 8 - 4 ) < 3 ( 8 x + 7 - 4 ) + ( 2 x + 6 x - 9 ) - 8 ( 4 x - 7 )$$

Solve for x

$$x<\frac{36}{25}$$

Solution Steps

Subtract 4 from 8 to get 4.

$$5\left(5x+4\right)<3\left(8x+7-4\right)+2x+6x-9-8\left(4x-7\right)$$

Use the distributive property to multiply 5 by 5x+4.

$$25x+20<3\left(8x+7-4\right)+2x+6x-9-8\left(4x-7\right)$$

Subtract 4 from 7 to get 3.

$$25x+20<3\left(8x+3\right)+2x+6x-9-8\left(4x-7\right)$$

Use the distributive property to multiply 3 by 8x+3.

$$25x+20<24x+9+2x+6x-9-8\left(4x-7\right)$$

Combine 24x and 2x to get 26x.

$$25x+20<26x+9+6x-9-8\left(4x-7\right)$$

Combine 26x and 6x to get 32x.

$$25x+20<32x+9-9-8\left(4x-7\right)$$

Subtract 9 from 9 to get 0.

$$25x+20<32x-8\left(4x-7\right)$$

Use the distributive property to multiply -8 by 4x-7.

$$25x+20<32x-32x+56$$

Combine 32x and -32x to get 0.

$$25x+20<56$$

Subtract 20 from both sides.

$$25x<56-20$$

Subtract 20 from 56 to get 36.

$$25x<36$$

Divide both sides by 25. Since 25 is positive, the inequality direction remains the same.

$$x<\frac{36}{25}$$