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

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
Simplify 7×8+1-7x+18.
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 by 8 and simplify.
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