Sure, let's solve the inequality [tex]\( 2x + 7 > 15 \)[/tex] step by step.
### Step 1: Subtract 7 from both sides
First, we need to isolate the term that contains [tex]\( x \)[/tex]. We can do this by subtracting 7 from both sides of the inequality:
[tex]\[ 2x + 7 - 7 > 15 - 7 \][/tex]
This simplifies to:
[tex]\[ 2x > 8 \][/tex]
### Step 2: Divide both sides by 2
Next, we want to solve for [tex]\( x \)[/tex], so we need to get rid of the coefficient 2 in front of [tex]\( x \)[/tex]. We do this by dividing both sides of the inequality by 2:
[tex]\[ \frac{2x}{2} > \frac{8}{2} \][/tex]
This simplifies to:
[tex]\[ x > 4 \][/tex]
### Conclusion
The solution to the inequality [tex]\( 2x + 7 > 15 \)[/tex] is:
[tex]\[ x > 4 \][/tex]
This means that [tex]\( x \)[/tex] must be greater than 4 for the inequality to hold true.
