The simplified inequality is n > −5.
To simplify the given inequality
1+8n>−2+5+7n−7, let's first combine like terms on both sides:
1+8n>3+7n−7.
Next, let's simplify further by subtracting
7n from both sides:
1+n>3−7.
Now, combine the constants on the right side:
1+n > −4.
Finally, subtract 1 from both sides to isolate
n: n > −5.
So, the simplified inequality is n>−5.
This means that any value of n greater than -5 will satisfy the original inequality.
In other words, if you substitute any number greater than -5 for n into the original expression, the inequality will hold true.
For example, if n=−4:
1+8(−4)>−2+5+7(−4)−7
−31>−28
This is true, confirming that n>−5 is the correct solution to the given inequality.
Question
Simplify the expression 1 + 8n > -2 + 5 + 7n - 7 .