Certainly! Let's solve the inequality step-by-step to determine the correct solution.
Given the inequality:
[tex]\[ 7x - 5 < 12x + 18 \][/tex]
### Step 1: Isolate all the [tex]\( x \)[/tex]-terms on one side
First, we'll move the [tex]\( 7x \)[/tex] term from the left side to the right side. We do this by subtracting [tex]\( 7x \)[/tex] from both sides of the inequality:
[tex]\[ 7x - 5 - 7x < 12x + 18 - 7x \][/tex]
This simplifies to:
[tex]\[ -5 < 5x + 18 \][/tex]
### Step 2: Isolate the variable term
Next, we need to isolate the [tex]\( x \)[/tex]-term by getting rid of the constant term on the right side. We do this by subtracting 18 from both sides:
[tex]\[ -5 - 18 < 5x + 18 - 18 \][/tex]
This simplifies to:
[tex]\[ -23 < 5x \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Now, to solve for [tex]\( x \)[/tex], we divide both sides of the inequality by 5:
[tex]\[ \frac{-23}{5} < x \][/tex]
Or equivalently:
[tex]\[ x > \frac{-23}{5} \][/tex]
### Final Answer
Thus, the solution to the inequality [tex]\( 7x - 5 < 12x + 18 \)[/tex] is:
[tex]\[ x > -\frac{23}{5} \][/tex]
Among the provided options, this corresponds to:
[tex]\[ b. \ x > -23 / 5 \][/tex]
So, the correct answer is:
[tex]\[ b. \ x > -23 / 5 \][/tex]
