Question

solve the inequality -5(x-7)<15 algebraically for x


-5(x-7)<15
-5x+35<15
-35 -35
-5x,-25
-5 -5 divide both sides by -5
x=5
is this correct?
Thanks for checking my work.

Answer 1

No, x=5 is not correct. The solution set to an inequality is an interval, not just a single point.

Your logic should have been:
-5(x-7) < 15
-5x+35 < 15
-5x < -20
x > 4

You could have checked your answer to see that x=5 works, but it is not the only number which does. In fact, any number x>4 makes the value in the parentheses greater than -3, so -5 times that is less than 15.

Note the change in direction of the inequality when multiplying/dividing by a negative value. This is just a shorthand way of moving the values to the other side. We could have done

-5x < -20
0 < 5x - 20
20 < 5x
4 < x