I need help a little bit on my math.
1. 6> - 2/3(7x-2)
2. -1/3(x - 9) + 4 < - 2
3. -1/4 x - 8 < 3/4
they work just like equations , except there is an inequality sign
... if you multiply or divide by a negative quantity , the arrow is reversed
1. 6 > - 2/3(7x-2)
6 > -14x/3+4/3
Multiply both sides by 3:
18 > -14x + 4
14 > -14x
Divide both sides by -14 and reverse inequality sign.
-1 < X.
Prob. #2 and #3 are similar to #1.
Certainly! I can help you with your math questions. Let's tackle them one by one.
1. To solve the inequality 6 > -2/3(7x - 2), we need to isolate the variable x. Here's the step-by-step process:
First, distribute -2/3 to the expression (7x - 2):
6 > (-2/3 * 7x) + (-2/3 * -2)
6 > (-14/3)x + 4/3
Next, simplify the expression:
6 > (-14/3)x + 4/3
Now, let's get rid of the fractions by multiplying the entire inequality by 3 to clear the denominators:
18 > -14x + 4
Rearrange the inequality so that the x term is on the left:
-14x + 4 < 18
Subtract 4 from both sides to get -14x by itself:
-14x < 14
Finally, divide both sides of the inequality by -14. Remember to reverse the inequality sign when dividing by a negative number:
x > -1
Therefore, the solution to the inequality is x > -1.
2. Now let's solve the inequality -1/3(x - 9) + 4 < -2:
Start by distributing -1/3 to the expression (x - 9):
(-1/3 * x) + (-1/3 * -9) + 4 < -2
-1/3x + 3 + 4 < -2
Combine like terms:
-1/3x + 7 < -2
Subtract 7 from both sides to isolate the variable:
-1/3x < -9
To get rid of the fraction, multiply the entire inequality by -3 to clear the denominator. Remember to reverse the inequality sign:
(-1/3x) * -3 > -9 * -3
1x > 27
Simplify the expression:
x > 27
Therefore, the solution to the inequality is x > 27.
3. Lastly, let's solve the inequality -1/4x - 8 < 3/4:
Begin by adding 8 to both sides to isolate the variable and get rid of the constant term:
-1/4x - 8 + 8 < 3/4 + 8
-1/4x < 27/4
To eliminate the fraction, multiply the entire inequality by -4. Don't forget to flip the inequality sign when multiplying by a negative number:
(-1/4x) * -4 > (27/4) * -4
x > -27/4
Simplify the expression:
x > -6.75
Therefore, the solution to the inequality is x > -6.75.
I hope that helps! If you have any further questions or need additional assistance, feel free to ask.