Here are the steps in solving the equation
7x+5 = 2x+35
7x-2x = 35-5
5x = 30
x = 30/5
x = 6
And here are the steps to solving the inequality
7x+5 > 2x+35
7x-2x > 35-5
5x > 30
x > 30/5
x > 6
The two batches of steps are nearly identical. All I've done is replaced the equal sign with the > sign. The inequality sign stays the same the entire time since we didn't multiply or divide both sides by a negative number.
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In short, Noah's solution of x = 6 is changed to x > 6.
Though this trick only works if we don't multiply or divide both sides by a negative number.