5(3+4x)-6>=129
I get 2 different answers on this one.
15+20x-6>=129
15+20x-6+6>=129+6
15+20x>=135
15-15+20x>=135-15
20x>=120
20x/20>=120/20
x>=6
Is this worked out properly, are there any shortcuts?
5(3+4x)-6>=129
15+20x-6>=129
9+20x>=129
20x>=120
x>=6
The steps you took in solving the inequality are correct. However, there is a slight shortcut you can take to simplify the equation. Let's go through the steps together:
1. Start with the original inequality: 5(3+4x)-6>=129
2. First, distribute the 5 to the terms inside the parentheses: 15+20x-6>=129
3. Combine like terms, which simplifies the equation: 9+20x>=129
4. To isolate the variable x, subtract 9 from both sides: 20x>=120
5. Divide both sides by 20 to solve for x: x>=6
So, your final answer x>=6 is correct. Keep in mind that when dividing or multiplying both sides of an inequality by a negative number, the inequality symbol must be flipped. In this case, since we divided by a positive number (20), we don't need to flip the inequality symbol.
It is essential to be careful and double-check your steps when solving inequalities to avoid any errors. Great job on correctly solving this inequality!