What is the next step after 20x > -7 in solving the inequality?
Understand the Problem
The question involves solving an inequality step by step, specifically reaching the conclusion presented in Step 8. The user is likely seeking clarification on the solution process or verification of their work leading to the final inequality.
Answer
$$ x > -\frac{7}{20} $$
Answer for screen readers
$$ x > -\frac{7}{20} $$
Steps to Solve
- Rearrange the Inequality Start with the original inequality: $$ 12x + 6 > -8x - 1 $$
Subtract 6 from both sides: $$ 12x > -8x - 7 $$
- Combine Like Terms Next, add $8x$ to both sides to combine like terms: $$ 12x + 8x > -7 $$
This simplifies to: $$ 20x > -7 $$
-
Isolate x To solve for $x$, divide both sides of the inequality by 20: $$ x > -\frac{7}{20} $$
-
Rewrite the final result This can be rewritten as: $$ 1x > \frac{7}{20} $$
$$ x > -\frac{7}{20} $$
More Information
In the context of inequalities, this solution indicates that $x$ must be greater than $-\frac{7}{20}$ for the original inequality to hold true. This kind of inequality shows us the range of possible values for $x$.
Tips
- Failing to change the direction of the inequality when multiplying or dividing by a negative number (which isn't applicable here but is important to remember in general).
- Miscalculating terms while combining like terms.
AI-generated content may contain errors. Please verify critical information
