x/4<9
x<9*4=36
x<36
a/9>or equal to -15
a> or equal too -135
-p/7>-9
-p>-63
p<-63
-t/12> or equal too 6
-t> or equal to 72
t< or equal too 72
how do u do these
-y<36
= y>36
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
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: ?
negative 12 times a number is no more than 84
define a variable:
write an inequality: -12n<84
solve: n>-7
negative one sizth of a number is less than -9
define a variable:
write an inequality: -1/6n<-9
solve: ?
eight times a number is at least 16
define:
inequality: 8n>16
solve:n>2
To solve inequalities like these, we can use similar techniques as solving equations. The main difference is that when multiplying or dividing by a negative number, the direction of the inequality sign must be reversed.
1. First, let's solve the inequality x/4 < 9:
Multiply both sides of the inequality by 4 (which is the denominator of x/4):
(x/4) * 4 < 9 * 4
Simplify:
x < 36
Thus, the solution is x < 36.
2. Now, let's solve the inequality a/9 ≥ -15:
Multiply both sides of the inequality by 9:
(a/9) * 9 ≥ -15 * 9
Simplify:
a ≥ -135
So, the solution is a ≥ -135.
3. Next, let's solve the inequality -p/7 > -9:
Multiply both sides of the inequality by 7 (note that the inequality sign is reversed since we multiply by a negative number):
(-p/7) * 7 < -9 * 7
Simplify:
-p < -63
Multiply both sides of the inequality by -1 (to isolate p):
-p * (-1) > -63 * (-1)
Simplify:
p > 63
Therefore, the solution is p > 63.
4. Lastly, let's solve the inequality -t/12 ≥ 6:
Multiply both sides of the inequality by 12 (note that the inequality sign does not change since we multiply by a positive number):
(-t/12) * 12 ≥ 6 * 12
Simplify:
-t ≥ 72
Multiply both sides of the inequality by -1 (to isolate t):
-t * (-1) ≤ 72 * (-1)
Simplify:
t ≤ -72
Thus, the solution is t ≤ -72.
Remember, to solve inequalities, we perform operations on both sides to isolate the variable using the rules you have learned in algebra.