Final answer:
The question asks for the lowest integer value of w that satisfies the inequality 6w + 3 > 29 – 4w. After simplifying the algebra, we find that w must be greater than 2.6, meaning the lowest integer value for w is 3. However, this answer is not listed in the given options, suggesting an error in the question.
Step-by-step explanation:
To solve for the lowest integer value of w, we need to solve the inequality 6w + 3 > 29 – 4w. First, we'll eliminate terms wherever possible to simplify the algebra:
Add 4w to both sides: 6w + 4w + 3 > 29
Combine like terms: 10w + 3 > 29
Subtract 3 from both sides: 10w > 26
Divide by 10 to isolate w: w > 2.6
Since we need the lowest integer value for w, and w must be greater than 2.6, the smallest integer that satisfies this condition is 3. However, we must check the answer to make sure it's reasonable. Substituting w = 3 into the original inequality gives 6(3) + 3 > 29 – 4(3), which simplifies to 18 + 3 > 29 - 12, or 21 > 17, which is true. Thus, the lowest integer value for w is 3, which is not listed in the given options, implying a typo in the question or the options provided.