Question

here is a diagram and its corresponding equation. find the solution to the equation.

6x + 11 = 21

x = __

Explanation:

Step1: Subtract 11 from both sides

To isolate the term with \( x \), we subtract 11 from both sides of the equation \( 6x + 11 = 21 \). This gives us \( 6x + 11 - 11 = 21 - 11 \), which simplifies to \( 6x = 10 \).

Step2: Divide both sides by 6

Now, to solve for \( x \), we divide both sides of the equation \( 6x = 10 \) by 6. So, \( x=\frac{10}{6} \), which simplifies to \( x = \frac{5}{3} \) (or approximately \( x \approx 1.67 \) if we want a decimal). Wait, no, wait, let's check again. Wait, 21 - 11 is 10? Wait, no, 21 - 11 is 10? Wait, 21 - 11 is 10? Wait, 6x + 11 = 21. Subtract 11: 6x = 21 - 11 = 10? Wait, no, 21 - 11 is 10? Wait, 21 - 11 is 10? Wait, no, 21 - 11 is 10? Wait, 6x = 10? Then x = 10/6 = 5/3? Wait, but maybe I made a mistake. Wait, the diagram: 6 x's and then 11, total 21. So 6x + 11 = 21. So subtract 11: 6x = 10? Wait, 21 - 11 is 10? Yes. Then divide by 6: x = 10/6 = 5/3 ≈ 1.666... But wait, maybe the diagram is 6 x's and then 11, total 21. Wait, maybe I misread the number of x's. Wait, the diagram has 6 x's? Wait, the boxes: x x x x x x, that's 6 x's, then the blue part is 11, total 21. So 6x + 11 = 21. So solving: 6x = 21 - 11 = 10. Then x = 10/6 = 5/3. Wait, but maybe the problem is 6x + 11 = 21, so x = (21 - 11)/6 = 10/6 = 5/3. Wait, but let's check again. Wait, 6x + 11 = 21. Subtract 11: 6x = 10. Divide by 6: x = 10/6 = 5/3. Yes.

Wait, no, wait, maybe I made a mistake in the subtraction. 21 - 11 is 10? Yes. 6x = 10. So x = 10/6 = 5/3. So the solution is x = 5/3 or x ≈ 1.67. But let's do it again.

Step1: Subtract 11 from both sides

\( 6x + 11 - 11 = 21 - 11 \)
\( 6x = 10 \)

Step2: Divide both sides by 6

\( x = \frac{10}{6} \)
Simplify the fraction: \( x = \frac{5}{3} \) (or as a decimal, \( x \approx 1.67 \))

Wait, but maybe the problem is 6x + 11 = 21, so x = (21 - 11)/6 = 10/6 = 5/3. So the solution is \( x = \frac{5}{3} \) or \( x \approx 1.67 \).

But let's check with the diagram. 6 times (5/3) is 10, plus 11 is 21. Yes, 6*(5/3) = 10, 10 + 11 = 21. Correct.

Answer:

\( \frac{5}{3} \) (or \( 1.\overline{6} \) as a repeating decimal)