Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our 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]
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.