Solve the inequality for x.
-28+5(7-x)≤-2(x+4)
Simplify your answer as much as possible.
Starting with the inequality -28 + 5(7 - x) ≤ -2(x + 4), we can simplify it step by step:
-28 + 5(7 - x) ≤ -2(x + 4)
-28 + 35 - 5x ≤ -2x - 8
7 - 5x ≤ -2x - 8
Adding 5x to both sides:
7 - 5x + 5x ≤ -2x - 8 + 5x
7 ≤ -2x - 8 + 5x
Simplifying:
7 ≤ 3x - 8
Adding 8 to both sides:
7 + 8 ≤ 3x - 8 + 8
15 ≤ 3x
Dividing by 3 (since it's positive) to isolate x:
15/3 ≤ 3x/3
5 ≤ x
So the solution is x ≥ 5.
To solve the inequality -28 + 5(7 - x) ≤ -2(x + 4), first simplify the expression on both sides of the inequality.
On the left side:
-28 + 5(7 - x) simplifies to -28 + 35 - 5x.
-28 + 35 - 5x simplifies to 7 - 5x.
On the right side:
-2(x + 4) simplifies to -2x - 8.
Now the inequality becomes:
7 - 5x ≤ -2x - 8.
To solve for x, let's isolate the x terms on one side and the constant terms on the other side.
Add 5x to both sides:
(7 - 5x) + 5x ≤ (-2x - 8) + 5x.
Simplifying both sides:
7 ≤ 3x - 8.
To isolate the x term, add 8 to both sides:
7 + 8 ≤ 3x - 8 + 8.
Simplifying both sides:
15 ≤ 3x.
Divide both sides by 3:
15/3 ≤ 3x/3.
Simplifying both sides:
5 ≤ x.
Thus, the solution to the inequality -28 + 5(7 - x) ≤ -2(x + 4) is x ≥ 5.
To solve the inequality -28 + 5(7 - x) ≤ -2(x + 4), we need to simplify the expressions first.
Step 1: Distribute the multiplication on both sides of the equation:
-28 + 35 - 5x ≤ -2x - 8
Step 2: Combine like terms:
7 - 5x ≤ -2x - 8
Step 3: Add 5x to both sides to isolate the x terms:
7 ≤ 3x - 8
Step 4: Add 8 to both sides to isolate the constant term:
15 ≤ 3x
Step 5: Divide both sides by 3 to solve for x:
15/3 ≤ x
5 ≤ x
Therefore, the solution to the inequality -28 + 5(7 - x) ≤ -2(x + 4) is x ≥ 5.