lve the inequality, if possible.
3(1+x)≥12−2x
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The solution is enter your response here.
(Type an inequality. Simplify your answer.)
B.
The solution is all real numbers.
C.
There is no solution.
Help me solve thisTextbook Get more help
Clear all
Check answer
To solve the inequality, let's simplify both sides:
3(1+x) ≥ 12 - 2x
First, distribute the 3 on the left side:
3 + 3x ≥ 12 - 2x
Combine like terms:
5x + 3 ≥ 12
Subtract 3 from both sides:
5x ≥ 9
Finally, divide both sides by 5 to solve for x:
x ≥ 9/5 or x ≥ 1.8
So the solution to the inequality is x ≥ 1.8.
Therefore, the correct choice is A. The solution is x ≥ 1.8.
To solve the given inequality:
3(1 + x) ≥ 12 - 2x
First, distribute 3 to both terms inside the parentheses:
3 + 3x ≥ 12 - 2x
Next, combine like terms:
3x + 2x ≥ 12 - 3
5x ≥ 9
To isolate x, divide both sides of the inequality by 5:
x ≥ 9/5
Therefore, the solution to the inequality is:
A. x ≥ 9/5
To solve the inequality 3(1+x) ≥ 12-2x, we can follow these steps:
Step 1: Distribute the 3 on the left side of the inequality:
3 + 3x ≥ 12 - 2x
Step 2: Combine like terms on both sides:
3x + 2x ≥ 12 - 3
5x ≥ 9
Step 3: Divide both sides of the inequality by 5 to isolate x:
x ≥ 9/5
So the solution to the inequality is x ≥ 9/5.
You can also represent this solution as an interval notation: [9/5, +∞).
Therefore, the correct choice is A. The solution is x ≥ 9/5.