Can someone please help me with this? I'm not looking for the answer, just a detailed explanation on how to solve this.
Thank you in advance.
Solve: 16(t - 1) + 10 > 8(t +2) + 4(t - 1) + 4t
Get rid of the parentheses and combine terms, e.g., 16(t-1) = 16t-16. Once this is done, combine like terms and put the x terms on one side of the inequality.
That makes more sense. Thank you!
Sure, I can help you with that.
To solve the given equation: 16(t - 1) + 10 > 8(t + 2) + 4(t - 1) + 4t
Step 1: Distribute the terms on both sides of the equation
On the left side, distribute the 16 to (t - 1): 16t - 16 + 10 > 8(t + 2) + 4(t - 1) + 4t
So, the left side of the equation becomes 16t - 6.
On the right side, distribute the 8 to (t + 2): 8t + 16
Also, distribute the 4 to (t - 1): 4t - 4
So, the right side of the equation becomes 8t + 16 + 4t - 4 + 4t.
Simplifying the right side further, we get: 16t + 12
Now, our equation is: 16t - 6 > 16t + 12
Step 2: Collect like terms
In this equation, we have 16t on both sides, which means it cancels out.
So, we are left with: -6 > 12
Step 3: Solve for the variable
Since -6 is not greater than 12, this inequality is not true. Therefore, there is no solution for the given equation.
So, the solution is an empty set {}.
Remember to double-check your work and make sure you haven't made any calculation errors along the way.