Question
-3x + 8 > 44 explained
Answers
GPT-4o mini
To solve the inequality \(-3x + 8 > 44\), follow these steps:
1. **Isolate the term with the variable:** Subtract 8 from both sides of the inequality to move the constant to the right side.
\[
-3x + 8 - 8 > 44 - 8
\]
This simplifies to:
\[
-3x > 36
\]
2. **Solve for \(x\):** Next, divide both sides by \(-3\). When you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign.
\[
x < \frac{36}{-3}
\]
Simplifying this gives:
\[
x < -12
\]
So, the solution to the inequality \(-3x + 8 > 44\) is:
\[
x < -12
\]
This means that any value of \(x\) that is less than \(-12\) will satisfy the original inequality.
1. **Isolate the term with the variable:** Subtract 8 from both sides of the inequality to move the constant to the right side.
\[
-3x + 8 - 8 > 44 - 8
\]
This simplifies to:
\[
-3x > 36
\]
2. **Solve for \(x\):** Next, divide both sides by \(-3\). When you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign.
\[
x < \frac{36}{-3}
\]
Simplifying this gives:
\[
x < -12
\]
So, the solution to the inequality \(-3x + 8 > 44\) is:
\[
x < -12
\]
This means that any value of \(x\) that is less than \(-12\) will satisfy the original inequality.