Solve 48<8(7-5n)-8(2n-1)

$$48 < 8 ( 7 - 5 n ) - 8 ( 2 n - 1 )$$

Solve for n

$$n<\frac{2}{7}$$

Solution Steps

Use the distributive property to multiply 8 by 7-5n.

$$48<56-40n-8\left(2n-1\right)$$

Use the distributive property to multiply -8 by 2n-1.

$$48<56-40n-16n+8$$

Combine -40n and -16n to get -56n.

$$48<56-56n+8$$

Add 56 and 8 to get 64.

$$48<64-56n$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$64-56n>48$$

Subtract 64 from both sides.

$$-56n>48-64$$

Subtract 64 from 48 to get -16.

$$-56n>-16$$

Divide both sides by -56. Since -56 is negative, the inequality direction is changed.

$$n<\frac{-16}{-56}$$

Reduce the fraction \frac{-16}{-56} to lowest terms by extracting and canceling out -8.

$$n<\frac{2}{7}$$