Solve the compound inequality.
-9 (less than or equal to) -3x - 9 (less than or equal to) 15
I totally forget how to solve inequalities, please help! Thanks!
-9<= -3x-9<=15
add 9 to each component.
0<=-3x<=24
divide by -3
0>x>8
check that.
This is what I got:
0(greater than or equal to)x(greater than or equal to) -8
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
(less than or equal to)=(LTorET)
(greater than or equal to)=(GTorET)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1. I broke it up into 2 problems
-9(LTorET)-3x-9 and -3x-9(LTorET)15
2.I solved the first problem by adding 9 to both sides. Then I had
0(LTorET)-3x
3.I divided both sides by -3 which equaled
0(GTorET)x
~~note: Flip the sign when dividing or multiplying by a negative~~
4. I did the same type of thing with
-3x-9(LTorET)15 which equaled
x(GTorET)-8
5. I got the answer:
0(GTorET)x(GTorET)-8
OR
x(LTorET)0 and x(GTorET)-8
~~however you want to write that~~
If you go to google and look up how to solve compound inequalities there are some good pages there.
-8 on the right is correct.
To solve a compound inequality, you will need to separate it into two separate inequalities and solve each one individually. Let's break down the given inequality step by step.
-9 ≤ -3x - 9 ≤ 15
Step 1: Start by isolating the variable term in the middle.
Add 9 to all parts of the inequality to isolate the -3x term:
-9 + 9 ≤ -3x - 9 + 9 ≤ 15 + 9
0 ≤ -3x ≤ 24
Step 2: Divide all parts of the inequality by the coefficient of x, which is -3. Remember that when you divide or multiply an inequality by a negative number, you must reverse the direction of the inequality symbols.
0/(-3) ≥ -3x/(-3) ≥ 24/(-3)
0 ≥ x ≥ -8
So, the solution to the compound inequality -9 ≤ -3x - 9 ≤ 15 is x between -8 and 0 inclusive.
In interval notation, the solution is given as: [-8, 0].