-5x + 2 ≤ 22
Understand the Problem
The question is asking to solve the inequality -5x + 2 ≤ 22 and likely to graph the solution on the number line provided. The approach will involve isolating x and determining the values that satisfy the inequality.
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 $x$, we first subtract $2$ from both sides of the inequality: $$ -5x + 2 - 2 \leq 22 - 2 $$ This simplifies to: $$ -5x \leq 20 $$
- Divide by the coefficient of x
Next, we divide both sides by $-5$. Remember, when we divide by a negative number, we must reverse the inequality sign: $$ x \geq \frac{20}{-5} $$ This simplifies to: $$ x \geq -4 $$
- Graph the solution on the number line
The solution $x \geq -4$ means that $x$ can be any value greater than or equal to $-4$. We plot a closed circle on $-4$ (to indicate inclusion) and shade to the right to represent all values greater than $-4$.
The solution to the inequality is $x \geq -4$.
More Information
This inequality represents all numbers greater than or equal to $-4$. The inclusion of $-4$ is shown by a closed circle in a graph on the number line.
Tips
- Forgetting to reverse the inequality sign when dividing by a negative number. Always check the direction of the inequality when performing operations involving negative numbers.
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