1. 5x+2>3x+10
=x>4
2. 8+2x< or equal too 6x-20
x> or equal too 7
3. 4(1-3n)-14>4(2n+3)-9n
=?
4-12n-14>8n+12-9n
5. x/4<9
x<9*4=36
x<36
6. a/9>or equal to -15
a> or equal too -135
7. -p/7>-9
-p>-63
p<-63
8. -t/12> or equal too 6
-t> or equal to 72
t< or equal too 72
9. -y<36
= y>36
10. define a variable, write an inequality, and solve each problem. check your solution
1. four times a number is greater than -48
define a variable:
write an inequality: 4n>-48
solve: n>-12
11. one eighth of a number is less than or equal too 3
define a variable:
write an inequality: 1/8 n < or equal too 3
solve: ?
12. negative 12 times a number is no more than 84
define a variable:
write an inequality: -12n<84
solve: n>-7
13. negative one sizth of a number is less than -9
define a variable:
write an inequality: -1/6n<-9
solve: ?
14. eight times a number is at least 16
define:
inequality: 8n>16
solve:n>2
First, that's equal to, NOT too!
It's a lot easier just to write x >= 2.
With that said, let's proceed.
#1: ok
#2: ok
#3: Hmmm. This one is no harder than the first two, just a bit longer.
4(1-3n)-14>4(2n+3)-9n
4-12n-14 > 8n+12-9n
-12n-10 > -n+12
-11n > 22
n < -2
#5,6: ok
#7: oops - should have been
-p/7>-9
-p>-63
p<+63 since -63/-1 = +63
#8:same thing here. When you change sign, you must change it on both sides of the inequality, just as you would in an equation.
-t/12>=6
-t >= 72
t <= -72
#9: same again.
-y<36
y > -36
#10: ok
#11: You had trouble with this easy easy one? You got #5 ok, and it's just the same.
1/8 n <= 3
n <= 24
#12: "no more than" mean "less than or equal", not "less than", so
-12n <= 84
n >= -7
#13: again, just as easy as the others.
-1/6 n < -9
n > 54
#14: ok
Looks like you need to review working with negative values.
4-12n-14>8n+12-9n
4-12-14>8n-9n+12n
-22>11n
n=0.5
11. define a variable:
Let n be the number.
write an inequality: (1/8)n ≤ 3
solve:
Multiply both sides by 8 to get rid of the fraction:
n ≤ 24
Check:
Choose a value for n that is less than or equal to 24, for example, n = 20.
(1/8)(20) = 2.5 which is less than or equal to 3.
So, the solution n ≤ 24 is correct.
13. define a variable:
Let n be the number.
write an inequality: (-1/6)n < -9
solve:
Multiply both sides by -6 to get rid of the fraction and to change the direction of the inequality:
n > -54
Check:
Choose a value for n that is greater than -54, for example, n = -50.
(-1/6)(-50) = 8.33, which is greater than -9.
So, the solution n > -54 is correct.
To solve the inequality in question 3, let's go step by step:
3. 4(1-3n)-14 > 4(2n+3)-9n
First, let's simplify both sides of the inequality:
On the left side:
4(1-3n) - 14 = 4 - 12n - 14 = -12n - 10
On the right side:
4(2n+3) - 9n = 8n + 12 - 9n = -n + 12
Now let's rewrite the inequality with the simplified expressions:
-12n - 10 > -n + 12
To solve for n, we need to isolate n on one side of the inequality. Let's start by getting rid of the -n on the right side by adding n to both sides:
-12n - 10 + n > 12
Simplifying further:
-11n - 10 > 12
Next, let's isolate the variable n by getting rid of the -10 on the left side by adding 10 to both sides:
-11n > 12 + 10
Simplifying further:
-11n > 22
Now, to isolate n, we need to divide both sides of the inequality by -11. When dividing by a negative number, remember to reverse the inequality symbol:
n < -22/11
Simplifying further:
n < -2
Therefore, the solution to the inequality is n < -2.