-5x + 2 ≤ 22
Understand the Problem
The question involves solving the inequality -5x + 2 ≤ 22. It seeks to determine the value or range of values for x that satisfy this condition.
Answer
\( x \geq -4 \)
Answer for screen readers
The solution to the inequality is ( x \geq -4 ).
Steps to Solve
- Isolate the term with x
To isolate the term with ( x ), subtract 2 from both sides of the inequality:
$$ -5x + 2 - 2 \leq 22 - 2 $$
This simplifies to:
$$ -5x \leq 20 $$
- Divide by -5
Next, divide both sides of the inequality by -5. Remember, when dividing or multiplying an inequality by a negative number, the direction of the inequality sign changes:
$$ \frac{-5x}{-5} \geq \frac{20}{-5} $$
This simplifies to:
$$ x \geq -4 $$
- Graph the solution
To graph the solution ( x \geq -4 ) on a number line, you would place a closed circle at -4 (indicating that -4 is included in the solution) and shade the line to the right, showing all the numbers greater than -4.
The solution to the inequality is ( x \geq -4 ).
More Information
This means that any value of ( x ) that is -4 or greater will satisfy the inequality. The inequality includes -4 itself since it is a "less than or equal to" situation.
Tips
- A common mistake is forgetting to reverse the inequality sign when dividing by a negative number. Always remember to switch the inequality direction when doing so.
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