Question

solve the inequality and graph the solution.
1 + 3w ≥ 7
plot the endpoints. select an endpoint to change it from closed to open. select the middle of
the segment, ray, or line to delete it.
-5 -4 -3 -2 -1 0 1 2 3 4 5
submit

Explanation:

Step1: Subtract 1 from both sides

To isolate the term with \( w \), we subtract 1 from both sides of the inequality \( 1 + 3w \geq 7 \). This gives us \( 1 + 3w - 1 \geq 7 - 1 \), which simplifies to \( 3w \geq 6 \).

Step2: Divide both sides by 3

To solve for \( w \), we divide both sides of the inequality \( 3w \geq 6 \) by 3. This gives us \( \frac{3w}{3} \geq \frac{6}{3} \), which simplifies to \( w \geq 2 \).

Answer:

The solution to the inequality \( 1 + 3w \geq 7 \) is \( w \geq 2 \). To graph this, we plot a closed circle at \( 2 \) (since the inequality is "greater than or equal to") and draw a ray to the right (towards positive infinity) from \( 2 \).