7×8+1>7x+18

Move 7x+18 to the left side of the equation by subtracting it from both sides.

7×8+1-7x+18>0

Combine fractions with similar denominators.

1+7x-(7x+1)8>0

Apply the distributive property.

1+7x-(7x)-1⋅18>0

Multiply.

Multiply 7 by -1.

1+7x-7x-1⋅18>0

Multiply -1 by 1.

1+7x-7x-18>0

1+7x-7x-18>0

Subtract 7x from 7x.

1+0-18>0

Simplify the expression.

Subtract 1 from 0.

1+-18>0

Move the negative in front of the fraction.

1-18>0

Write 1 as a fraction with a common denominator.

88-18>0

Combine the numerators over the common denominator.

8-18>0

8-18>0

Subtract 1 from 8.

78>0

78>0

Since this is the only denominator in the list, the result is the LCD: 8.

8

Multiply each term in 78>0 by 8.

78⋅8>0⋅8

Cancel the common factor of 8.

Cancel the common factor.

78⋅8>0⋅8

Rewrite the expression.

7>0⋅8

7>0⋅8

Multiply 0 by 8.

7>0

7>0

Since 7>0, the inequality will always be true for any value of x.

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

(-∞,∞)

Solve for x (7x)/8+1>(7x+1)/8