When solving the inequality 10x + 22 < 2, the second step should say 10x > −20 because I added -22 to both sides and I got a negative number on the right.
Is this correct?
correct so far.
Now divide both sides by 10
since you dividing by a positive 10, the inequality sign stays as >
x > -2!
Is that correct?
yes
No, the statement that "10x + 22 < 2" becomes "10x > -20" after adding -22 to both sides is not correct. Let me explain the correct steps to solve this inequality.
To solve the inequality 10x + 22 < 2, we need to isolate the variable x. Here are the correct steps:
Step 1: Subtract 22 from both sides of the inequality:
10x + 22 - 22 < 2 - 22
This simplifies to:
10x < -20
Now, we have the correct inequality 10x < -20. Since we want to solve for x, we divide both sides of the inequality by 10 (the coefficient of x):
Step 2: Divide both sides by 10:
10x/10 < -20/10
This simplifies to:
x < -2
Therefore, the correct solution to the inequality 10x + 22 < 2 is x < -2.
In summary, the correct second step is "10x < -20" after subtracting 22 from both sides, not "10x > -20".