Consider the inequality 3( - 1 - x) ≤ -2x - 3x.
The solution set of the inequality is:
(1 point)
Responses
{x|x≥32
}
{x|xis greater than or equal to 3 halves}
{x|x≤32
}
{x|xis less than or equal to 3 halves}
{x|x≥23
}
{x|xis greater than or equal to 2 thirds}
{x|x≤23
}
To solve the inequality 3(-1 - x) ≤ -2x - 3x, let's simplify the left side first:
3(-1 - x) = -3 - 3x
Substituting this back into the original inequality, we have:
-3 - 3x ≤ -2x -3x
Next, we can combine like terms on both sides:
-3 - 3x ≤ -5x
Now, let's isolate x by adding 3x to both sides:
-3 ≤ -5x + 3x
Simplifying further, we get:
-3 ≤ -2x
To solve for x, divide both sides by -2, remembering to reverse the inequality sign:
-3/-2 ≥ x
This simplifies to:
x ≥ 3/2
Therefore, the solution set of the inequality is:
{x | x ≥ 3/2}
{x|x≥3/2}
To solve the inequality 3(-1-x) ≤ -2x - 3x, follow these steps:
Step 1: Distribute the 3 on the left side of the inequality:
-3 - 3x ≤ -2x - 3x
Step 2: Combine like terms on both sides:
-3 - 3x ≤ -5x
Step 3: Add 5x to both sides to isolate the variable on one side:
5x - 3 - 3x + 5x ≤ -5x + 5x
2x - 3 ≤ 0
Step 4: Add 3 to both sides to get rid of the negative 3:
2x - 3 + 3 ≤ 0 + 3
2x ≤ 3
Step 5: Divide both sides by 2:
2x/2 ≤ 3/2
x ≤ 3/2
The solution to the inequality is x ≤ 3/2.
Thus, the correct solution set of the inequality is:
{x | x ≤ 3/2}