Solve the inequality, if possible.
3(2 + x) >= 14 - 2x
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The solution is _. (Type an inequality. Simplify your answer.)
OB. The solution is all real numbers.
OC. There is no solution.
To solve the inequality, we can start by distributing 3 to both terms inside the parentheses:
6 + 3x ≥ 14 - 2x
Next, we can combine like terms by adding 2x to both sides:
6 + 5x ≥ 14
Subtracting 6 from both sides gives us:
5x ≥ 8
Finally, we divide both sides by 5 to solve for x:
x ≥ 8/5
Therefore, the solution to the inequality is:
OA. The solution is x ≥ 8/5.
To solve the inequality 3(2 + x) ≥ 14 - 2x, we need to simplify and isolate the variable x.
Let's start by distributing the 3 on the left side:
6 + 3x ≥ 14 - 2x
Next, let's move all the terms involving x to one side:
3x + 2x ≥ 14 - 6
Combining like terms, we get:
5x ≥ 8
Now, to isolate x, we divide both sides of the inequality by 5:
x ≥ 8/5
So, the solution to the inequality is x ≥ 8/5.
Therefore, the correct choice is:
OA. The solution is x ≥ 8/5.
To solve the inequality 3(2 + x) >= 14 - 2x, we will follow these steps:
Step 1: Simplify both sides of the inequality:
2 + x can be simplified to 2x, so the inequality becomes:
3(2x) >= 14 - 2x
Step 2: Distribute 3 to 2x:
3 * 2x = 6x
The inequality now becomes:
6x >= 14 - 2x
Step 3: Combine like terms on the right side:
On the right side, we have 14 and -2x. We can combine these by adding -2x to 14, which gives us:
6x >= 14 - 2x
14 - 2x can be rewritten as -2x + 14.
Now the inequality becomes:
6x >= -2x + 14
Step 4: Add 2x to both sides to get the variables on one side:
On both sides of the inequality, we will add 2x:
6x + 2x >= -2x + 2x + 14
Simplifying this gives us:
8x >= 14
Step 5: Divide both sides by 8 to isolate the variable:
To solve for x, we need to isolate it on one side of the inequality. We can do this by dividing both sides by 8:
(8x)/8 >= 14/8
Simplifying further gives us:
x >= 7/4
So the solution to the inequality 3(2 + x) >= 14 - 2x is:
The solution is x >= 7/4. (OA)