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.
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You have defined the variable as x and written the inequality correctly as 7 - 2x < 3x + 32. To solve the inequality, you need to isolate the variable x on one side of the inequality sign.
Let's go step by step:
1. Start by getting rid of the constant term on the right side of the inequality. Subtract 32 from both sides:
7 - 2x - 32 < 3x + 32 - 32
-25 - 2x < 3x
2. Next, combine like terms on the left side by adding 2x to both sides:
-25 - 2x + 2x < 3x + 2x
-25 < 5x
3. Divide both sides of the inequality by 5 to solve for x:
-25 / 5 < 5x / 5
-5 < x
Therefore, the solution to the inequality is x > -5.
To check if your solution is correct, substitute a value greater than -5 for x in the original inequality and see if the inequality holds true. For example, let's substitute x = 0:
7 - 2(0) < 3(0) + 32
7 < 0 + 32
7 < 32
Since 7 is indeed less than 32, the inequality holds true. Hence, our solution x > -5 is correct.