define a variable, write an iquality, and solve the problem below. then check your solution.
"seven minus two times a number is less than three times the number plus thirty-two"
7-2*x<3x+32 is this right so far? what goes next?
Yes, you are right so far.
7 - 2x < 3x + 32
Treat it like a regular equation question.
Combine like terms and solve for x.
7 - 32 = 2x + 3x
-25 = 5x
-25/5 = x
-5 = x
Checking:
7 - 2x < 3x + 32
7 - 2(-5) < 3(-5) + 32
7 + 10 < -15 + 32
17 < 17....This is not true.
What does this mean? It means that there are no solutions to this inequality.
To solve the problem, you are on the right track with the inequality you created: 7 - 2x < 3x + 32. To solve it, follow these steps:
1. Start by isolating the variable on one side of the inequality. To do this, you'll need to get rid of the constant terms on both sides first. Begin by subtracting 7 from both sides:
7 - 7 - 2x < 3x + 32 - 7
Simplifying:
-2x < 3x + 25
2. Next, move the terms involving x to one side of the inequality by subtracting 3x from both sides:
-2x - 3x < 3x - 3x + 25
Simplifying:
-5x < 25
3. Now that the x variable is on one side, divide both sides by -5. Remember that dividing by a negative number flips the inequality sign:
(-5x) / (-5) > (25) / (-5)
Simplifying:
x > -5
So the solution to the inequality is x > -5.
To check your solution and ensure it is correct, you can substitute any value greater than -5 into the inequality and see if it holds true. Let's try x = 0:
7 - 2(0) < 3(0) + 32
7 < 32
Since 7 is indeed less than 32, the inequality holds true for x = 0. Therefore, the solution x > -5 is correct.