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.
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
Let's check your work:
-5(x-7)<15
-5x + 35 < 15
Subtracting 35 from both sides:
-5x < -20
Now, dividing both sides by -5:
x > 4
So the correct solution is x > 4, not x = 5.
Therefore, your work is incorrect.
You're very close! When dividing both sides of the inequality by -5, make sure to reverse the inequality symbol because you are dividing by a negative number.
So, starting from -5x + 35 < 15, the correct steps would be:
-5x + 35 < 15
-5x < 15 - 35
-5x < -20
Now, divide both sides of the inequality by -5, remembering to reverse the inequality symbol:
(-5x)/(-5) > (-20)/(-5)
x > 4
Therefore, the correct solution to the inequality -5(x-7) < 15 is x > 4.
Great job working through the problem! If you have any more questions, feel free to ask.