Certainly! Let's solve the inequality step-by-step.
We are given the inequality:
[tex]\[10x + 16 \geq 6x + 20\][/tex]
### Step 1: Simplify both sides of the inequality
First, let's move the [tex]\(6x\)[/tex] term from the right side to the left side by subtracting [tex]\(6x\)[/tex] from both sides:
[tex]\[10x + 16 - 6x \geq 6x + 20 - 6x\][/tex]
This simplifies to:
[tex]\[4x + 16 \geq 20\][/tex]
### Step 2: Isolate the variable
Next, we want to isolate the [tex]\(x\)[/tex] term. To do this, we'll subtract 16 from both sides:
[tex]\[4x + 16 - 16 \geq 20 - 16\][/tex]
This simplifies to:
[tex]\[4x \geq 4\][/tex]
### Step 3: Solve for [tex]\(x\)[/tex]
Finally, to solve for [tex]\(x\)[/tex], we'll divide both sides by 4:
[tex]\[\frac{4x}{4} \geq \frac{4}{4}\][/tex]
This simplifies to:
[tex]\[x \geq 1\][/tex]
### Conclusion
The solution to the inequality [tex]\(10x + 16 \geq 6x + 20\)[/tex] is:
[tex]\[x \geq 1\][/tex]
Therefore, the correct answer is:
A. [tex]\(x \geq 1\)[/tex]
