Answer :
To solve the inequality [tex]\(-3(x-3) \leq 5(1-x)\)[/tex], let's proceed step-by-step:
1. Expand both sides of the inequality:
Let's first expand the expressions on both sides of the inequality.
[tex]\[ -3(x - 3) \leq 5(1 - x) \][/tex]
For the left side:
[tex]\[ -3(x - 3) = -3x + 9 \][/tex]
For the right side:
[tex]\[ 5(1 - x) = 5 - 5x \][/tex]
2. Rewrite the inequality with the expanded expressions:
Now we have:
[tex]\[ -3x + 9 \leq 5 - 5x \][/tex]
3. Isolate the terms involving [tex]\(x\)[/tex] on one side of the inequality:
To simplify, let's add [tex]\(5x\)[/tex] to both sides:
[tex]\[ -3x + 5x + 9 \leq 5 - 5x + 5x \][/tex]
Which simplifies to:
[tex]\[ 2x + 9 \leq 5 \][/tex]
4. Isolate the constant term on the other side:
Subtract 9 from both sides:
[tex]\[ 2x + 9 - 9 \leq 5 - 9 \][/tex]
Which simplifies to:
[tex]\[ 2x \leq -4 \][/tex]
5. Solve for [tex]\(x\)[/tex]:
Finally, divide both sides by 2:
[tex]\[ x \leq \frac{-4}{2} \][/tex]
[tex]\[ x \leq -2 \][/tex]
Thus, the solution to the inequality [tex]\(-3(x-3) \leq 5(1-x)\)[/tex] is [tex]\(x \leq -2\)[/tex].
The correct answer is:
[tex]\[ \boxed{\text{C. } x \leq -2} \][/tex]
1. Expand both sides of the inequality:
Let's first expand the expressions on both sides of the inequality.
[tex]\[ -3(x - 3) \leq 5(1 - x) \][/tex]
For the left side:
[tex]\[ -3(x - 3) = -3x + 9 \][/tex]
For the right side:
[tex]\[ 5(1 - x) = 5 - 5x \][/tex]
2. Rewrite the inequality with the expanded expressions:
Now we have:
[tex]\[ -3x + 9 \leq 5 - 5x \][/tex]
3. Isolate the terms involving [tex]\(x\)[/tex] on one side of the inequality:
To simplify, let's add [tex]\(5x\)[/tex] to both sides:
[tex]\[ -3x + 5x + 9 \leq 5 - 5x + 5x \][/tex]
Which simplifies to:
[tex]\[ 2x + 9 \leq 5 \][/tex]
4. Isolate the constant term on the other side:
Subtract 9 from both sides:
[tex]\[ 2x + 9 - 9 \leq 5 - 9 \][/tex]
Which simplifies to:
[tex]\[ 2x \leq -4 \][/tex]
5. Solve for [tex]\(x\)[/tex]:
Finally, divide both sides by 2:
[tex]\[ x \leq \frac{-4}{2} \][/tex]
[tex]\[ x \leq -2 \][/tex]
Thus, the solution to the inequality [tex]\(-3(x-3) \leq 5(1-x)\)[/tex] is [tex]\(x \leq -2\)[/tex].
The correct answer is:
[tex]\[ \boxed{\text{C. } x \leq -2} \][/tex]
