Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

For each inequality on the left side, solve for [tex]x[/tex] and then match it to the correct answer on the right side. Each answer on the right side will be used once.

[tex]\[
\begin{array}{ll}
-2(2x + 5) \leq -7(x + 4) & x \geq -2 \\
\frac{4x - 6}{2} \geq 3x - 1 & x \leq -2 \\
5(x - 3) \leq 9(x + 1) & x \geq -6 \\
3(x - 4) + 5 \geq 2x - 9 & x \leq -6
\end{array}
\][/tex]

Sagot :

GinnyAnswer
Sure! Let's solve each inequality step-by-step to determine the correct answers.

### 1. Solve [tex]\( -2(2x + 5) \leq -7(x + 4) \)[/tex]

First, expand both sides:
[tex]\[ -2(2x + 5) = -4x - 10 \][/tex]
[tex]\[ -7(x + 4) = -7x - 28 \][/tex]

So the inequality becomes:
[tex]\[ -4x - 10 \leq -7x - 28 \][/tex]

Next, add [tex]\( 7x \)[/tex] to both sides:
[tex]\[ 3x - 10 \leq -28 \][/tex]

Then, add 10 to both sides:
[tex]\[ 3x \leq -18 \][/tex]

Finally, divide both sides by 3:
[tex]\[ x \leq -6 \][/tex]

Thus, [tex]\[ x \leq -6 \][/tex].

### 2. Solve [tex]\( \frac{4x - 6}{2} \geq 3x - 1 \)[/tex]

Simplify the fraction:
[tex]\[ 2x - 3 \geq 3x - 1 \][/tex]

Subtract [tex]\( 3x \)[/tex] from both sides:
[tex]\[ - x - 3 \geq -1 \][/tex]

Add 3 to both sides:
[tex]\[ - x \geq 2 \][/tex]

Multiply both sides by -1, and reverse the inequality sign:
[tex]\[ x \leq -2 \][/tex]

Thus, [tex]\[ x \leq -2 \][/tex].

### 3. Solve [tex]\( 5(x - 3) \leq 9(x + 1) \)[/tex]

First, expand both sides:
[tex]\[ 5(x - 3) = 5x - 15 \][/tex]
[tex]\[ 9(x + 1) = 9x + 9 \][/tex]

So the inequality becomes:
[tex]\[ 5x - 15 \leq 9x + 9 \][/tex]

Next, subtract [tex]\( 5x \)[/tex] from both sides:
[tex]\[ -15 \leq 4x + 9 \][/tex]

Then, subtract 9 from both sides:
[tex]\[ -24 \leq 4x \][/tex]

Finally, divide both sides by 4:
[tex]\[ -6 \leq x \][/tex]
or equivalently
[tex]\[ x \geq -6 \][/tex]

Thus, [tex]\[ x \geq -6 \][/tex].

### 4. Solve [tex]\( 3(x - 4) + 5 \geq 2x - 9 \)[/tex]

Expand:
[tex]\[ 3(x - 4) + 5 = 3x - 12 + 5 = 3x - 7 \][/tex]

So the inequality becomes:
[tex]\[ 3x - 7 \geq 2x - 9 \][/tex]

Subtract [tex]\( 2x \)[/tex] from both sides:
[tex]\[ x - 7 \geq -9 \][/tex]

Add 7 to both sides:
[tex]\[ x \geq -2 \][/tex]

Thus, [tex]\[ x \geq -2 \][/tex].

### Matching the inequalities to the solutions:

[tex]\[ \begin{array}{ll} -2(2 x+5) \leq-7(x+4) & x \leq-6 \\ \frac{4 x-6}{2} \geq 3 x-1 & x \leq-2 \\ 5(x-3) \leq 9(x+1) & x \geq-6 \\ 3(x-4)+5 \geq 2 x-9 & x \geq-2 \\ \end{array} \][/tex]

Thus, the correct matches are:
[tex]\[ \begin{array}{ll} -2(2 x+5) \leq-7(x+4) & x \leq-6 \\ \frac{4 x-6}{2} \geq 3 x-1 & x \leq-2 \\ 5(x-3) \leq 9(x+1) & x \geq-6 \\ 3(x-4)+5 \geq 2 x-9 & x \geq-2 \\ \end{array} \][/tex]
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.