Question

solve the inequality and graph the solution.
2 + 4r > -2
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
-5 -4 -3 -2 -1 0 1 2 3 4 5

Explanation:

Step1: Subtract 2 from both sides

To isolate the term with \( r \), we subtract 2 from both sides of the inequality \( 2 + 4r > -2 \). This gives us \( 2 + 4r - 2 > -2 - 2 \), which simplifies to \( 4r > -4 \).

Step2: Divide both sides by 4

To solve for \( r \), we divide both sides of the inequality \( 4r > -4 \) by 4. Since 4 is a positive number, the direction of the inequality sign remains the same. So we have \( \frac{4r}{4} > \frac{-4}{4} \), which simplifies to \( r > -1 \).

Answer:

The solution to the inequality \( 2 + 4r > -2 \) is \( r > -1 \). To graph this, we plot an open circle at \( -1 \) (because the inequality is strict, \( > \), not \( \geq \)) and draw an arrow to the right to indicate all values of \( r \) greater than \( -1 \).