Solve the inequality 5x + 6 > -9 for x.
Understand the Problem
The question asks to solve the linear inequality (5x + 6 > -9) for (x). This involves isolating (x) on one side of the inequality by performing algebraic operations, and simplifying the result as much as possible.
Answer
$x > -3$
Answer for screen readers
$x > -3$
Steps to Solve
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Isolate the term with $x$ Subtract 6 from both sides of the inequality to isolate the term with $x$: $$ 5x + 6 - 6 > -9 - 6 $$ $$ 5x > -15 $$
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Solve for $x$ Divide both sides of the inequality by 5 to solve for $x$: $$ \frac{5x}{5} > \frac{-15}{5} $$ $$ x > -3 $$
$x > -3$
More Information
The solution to the inequality $5x + 6 > -9$ is $x > -3$. This means that any value of $x$ greater than $-3$ will satisfy the original inequality.
Tips
A common mistake is forgetting to flip the inequality sign when dividing or multiplying by a negative number. However, in this problem, we divided by a positive number (5), so the inequality sign remains the same.
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