Answer :
To solve the inequality \(8x + 7 < 45x + 18\), we need to isolate \(x\) on one side of the inequality. Let's proceed with the steps:
1. Subtract \(8x\) from both sides of the inequality:
[tex]\[ 8x + 7 - 8x < 45x + 18 - 8x \][/tex]
This simplifies to:
[tex]\[ 7 < 37x + 18 \][/tex]
2. Subtract 18 from both sides to further isolate the term involving \(x\):
[tex]\[ 7 - 18 < 37x + 18 - 18 \][/tex]
This simplifies to:
[tex]\[ -11 < 37x \][/tex]
3. To solve for \(x\), divide both sides by 37:
[tex]\[ \frac{-11}{37} < x \][/tex]
This can be rewritten as:
[tex]\[ x > -\frac{11}{37} \][/tex]
Therefore, the solution to the inequality \(8x + 7 < 45x + 18\) is:
[tex]\[ x > -\frac{11}{37} \][/tex]
So, the correct answer is:
B. [tex]\(x > -\frac{11}{37}\)[/tex]
1. Subtract \(8x\) from both sides of the inequality:
[tex]\[ 8x + 7 - 8x < 45x + 18 - 8x \][/tex]
This simplifies to:
[tex]\[ 7 < 37x + 18 \][/tex]
2. Subtract 18 from both sides to further isolate the term involving \(x\):
[tex]\[ 7 - 18 < 37x + 18 - 18 \][/tex]
This simplifies to:
[tex]\[ -11 < 37x \][/tex]
3. To solve for \(x\), divide both sides by 37:
[tex]\[ \frac{-11}{37} < x \][/tex]
This can be rewritten as:
[tex]\[ x > -\frac{11}{37} \][/tex]
Therefore, the solution to the inequality \(8x + 7 < 45x + 18\) is:
[tex]\[ x > -\frac{11}{37} \][/tex]
So, the correct answer is:
B. [tex]\(x > -\frac{11}{37}\)[/tex]
