Question
1.7 Solve \( \leftarrow \begin{array}{l}\text { Question 7, 1.7.35 } \\ \text { Part } 1 \text { of } 2 \\ \text { Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number } \\ 8(x+1)+2 \geq 7 x+17 \\ \text { Select the correct choice below and, if necessary, fill in the answer box to complete your choice. } 11 \\ \text { A. The solution is } \square \text {. (Type the solution using interval notation.) } \\ \text { B. The solution set is } \varnothing \text {. }\end{array} \) Save 1 .
Ask by Vargas Brewer. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is [7, ∞).
Solution
To solve the inequality:
8(x + 1) + 2 ≥ 7x + 17
Step 1: Distribute and simplify the left-hand side.
8·x + 8·1 + 2 = 8x + 8 + 2 = 8x + 10
Now the inequality is:
8x + 10 ≥ 7x + 17
Step 2: Get all terms with x on one side by subtracting 7x from both sides.
8x + 10 – 7x ≥ 7x + 17 – 7x
Simplify:
x + 10 ≥ 17
Step 3: Isolate x by subtracting 10 from both sides.
x + 10 – 10 ≥ 17 – 10
Simplify:
x ≥ 7
Thus the solution set in interval notation is: [7, ∞).
Graphically, on the number line, shade all points starting at 7 (with a closed dot to indicate 7 is included) and extending to the right indefinitely.
Select answer choice:
A. The solution is [7, ∞).
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Simplify this solution Beyond the Answer
To solve the inequality \(8(x+1) + 2 \geq 7x + 17\), start by simplifying both sides. Expanding the left side gives \(8x + 8 + 2 \geq 7x + 17\), which simplifies to \(8x + 10 \geq 7x + 17\). Subtracting \(7x\) from both sides results in \(x + 10 \geq 17\). From here, you would subtract 10 from both sides, leading to \(x \geq 7\). Thus, in interval notation, the solution is \([7, \infty)\). When you graph this solution on a number line, start at 7 and shade everything to the right, indicating that all numbers greater than or equal to 7 are included in the solution. Use a closed dot on 7 to signify that it’s included in the solution set!
