Question

directions use this information to answer parts a and b. \\( 8c + 13 \geq 47 \\) \\( \text{part a} \\) solve the inequality by entering the correct answer in the box. \\( \text{show hints} \\) \\( \text{solution:} \\) \\( x \\) \\( 7 \\) \\( 8 \\) \\( 9 \\) \\( + \\) \\( = \\)

Explanation:

Step1: Subtract 13 from both sides

To isolate the term with \( x \), we subtract 13 from both sides of the inequality \( 8x + 13 \geq 47 \). This gives us \( 8x + 13 - 13 \geq 47 - 13 \), which simplifies to \( 8x \geq 34 \). Wait, no, 47 - 13 is 34? Wait, 47 - 13: 47 - 10 is 37, minus 3 more is 34? Wait, no, 13 + 34 is 47, yes. Wait, but then dividing by 8: \( x \geq \frac{34}{8} \)? Wait, no, maybe I misread the original inequality. Wait, the original problem: let me check again. The user's image shows "8c + 13 ≥ 47"? Wait, maybe it's 8x + 13 ≥ 47. Wait, let's do it correctly.

Wait, 8x + 13 ≥ 47. Subtract 13 from both sides: 8x ≥ 47 - 13. 47 - 13 is 34? No, 47 - 13: 47 - 10 = 37, 37 - 3 = 34? Wait, 13 + 34 = 47, yes. Then divide both sides by 8: x ≥ 34/8. Simplify 34/8: divide numerator and denominator by 2, get 17/4 = 4.25. Wait, but maybe the original inequality is 8x + 13 ≥ 47? Wait, maybe I made a mistake. Wait, let's check again.

Wait, 8x + 13 ≥ 47. Subtract 13: 8x ≥ 34. Then x ≥ 34/8 = 17/4 = 4.25. But maybe the original problem is 8x + 13 ≥ 47? Or maybe 8x + 13 ≥ 47. Wait, perhaps the user made a typo, but assuming it's 8x + 13 ≥ 47.

Wait, no, maybe the original inequality is 8x + 13 ≥ 47. Let's solve it step by step.

Step1: Subtract 13 from both sides

\( 8x + 13 - 13 \geq 47 - 13 \)
\( 8x \geq 34 \)

Step2: Divide both sides by 8

\( x \geq \frac{34}{8} \)
Simplify \( \frac{34}{8} \) to \( \frac{17}{4} \) or 4.25. But maybe the original inequality is 8x + 13 ≥ 47? Wait, maybe the variable is c? Let's check the image again. The image shows "8c + 13 ≥ 47". So it's 8c + 13 ≥ 47.

So let's correct that.

Step1: Subtract 13 from both sides

\( 8c + 13 - 13 \geq 47 - 13 \)
\( 8c \geq 34 \) Wait, no, 47 - 13 is 34? Wait, 47 - 13: 47 - 10 = 37, 37 - 3 = 34. Yes. Then divide both sides by 8: \( c \geq \frac{34}{8} = \frac{17}{4} = 4.25 \). But maybe the original inequality is 8c + 13 ≥ 47. Alternatively, maybe it's 8x + 13 ≥ 47.

Wait, maybe the user's problem is 8x + 13 ≥ 47. Let's solve it correctly.

Step1: Subtract 13 from both sides

\( 8x + 13 - 13 \geq 47 - 13 \)
\( 8x \geq 34 \)

Step2: Divide both sides by 8

\( x \geq \frac{34}{8} \)
Simplify \( \frac{34}{8} \) to \( \frac{17}{4} \) or 4.25. But maybe the original inequality is 8x + 13 ≥ 47. Alternatively, maybe the inequality is 8x + 13 ≥ 47.

Wait, maybe I misread the original problem. Let me check the image again. The user's image shows "8c + 13 ≥ 47" (maybe "c" is "x"). So let's solve 8x + 13 ≥ 47.

Step1: Subtract 13 from both sides

\( 8x \geq 47 - 13 \)
\( 8x \geq 34 \)

Step2: Divide both sides by 8

\( x \geq \frac{34}{8} \)
Simplify \( \frac{34}{8} \) to \( \frac{17}{4} \) or 4.25. But maybe the original problem is 8x + 13 ≥ 47. Alternatively, maybe the inequality is 8x + 13 ≥ 47.

Wait, maybe the user made a typo, but assuming it's 8x + 13 ≥ 47, the solution is x ≥ 17/4 or 4.25. But maybe the original inequality is 8x + 13 ≥ 47.

Alternatively, maybe the original inequality is 8x + 13 ≥ 47. Let's confirm:

8x + 13 ≥ 47

Subtract 13: 8x ≥ 34

Divide by 8: x ≥ 34/8 = 17/4 = 4.25

So the solution is x ≥ 17/4 or 4.25.

But maybe the original problem is 8x + 13 ≥ 47. So the solution is x ≥ 17/4 (or 4.25).

Answer:

\( x \geq \frac{17}{4} \) (or \( x \geq 4.25 \))