-1/4(d+1)<2
1. distribute everything inside the parentheses by multiplying -1/4 with d (-1/4*d) and with 1(-1/4): -1/4d-1/4<2
2. isolate -1/4d by cancelling the -1/4 (add 1/4 to 2): -1/4d<9/4 (2 and 1/4)
3. divide the 9/4 by -1/4 (for this we multiply by the flipped version of the number, -4). because you are dividing by a negative number, you must flip the inequality sign from < to >
4. d > -9
hope this helps!
shorter way:
-1/4(d+1)<2 <---- times 4
-(d+1) < 8
-d - 1 < 8
-d < 9
d > -9
To solve the inequality -1/4(d+1) < 2, we can follow these steps:
Step 1: Distribute the -1/4 to the terms inside the parentheses:
-1/4 * d - 1/4 * 1 < 2
Step 2: Simplify the equation:
-1/4d - 1/4 < 2
Step 3: Add 1/4 to both sides of the inequality to isolate the variable:
-1/4d < 2 + 1/4
Step 4: Combine like terms:
-1/4d < 9/4
Step 5: To get rid of the negative sign, we multiply both sides by -1 (since we are multiplying by a negative number, the inequality sign will flip):
(-1/4d) * -1 > (9/4) * -1
Simplifying further:
1/4d > -9/4
Step 6: Finally, to isolate the variable, we multiply both sides by 4/1:
(1/4d) * (4/1) > (-9/4) * (4/1)
Simplifying the equation:
d > -9/1
In conclusion, the solution to the inequality -1/4(d+1) < 2 is d > -9/1 or d > -9.