Question

clare drew this diagram to match the equation $2x + 16 = 50$, but she got the wrong solution as a result of using this diagram.
a. what value for $x$ can be found using the diagram?
$x = $
b. complete the statement about how clares diagram can be changed so that it correctly matches the equation.
the diagram correctly represents the equation if the first block is changed from 2 to
c. use the new diagram to find a correct value for $x$.

Explanation:

Step1: Solve for x from the diagram

The diagram shows $2 + x + 16 = 50$. Combine constants: $18 + x = 50$. Rearrange to solve for x:
$x = 50 - 18$

Step2: Calculate x for part a

$x = 32$

Step3: Fix the diagram for the equation

The correct equation is $2x + 16 = 50$, so the first block should be $x$ (to make two $x$ blocks total). Thus, change 2 to $x$.

Step4: Solve correct equation for part c

From $2x + 16 = 50$, subtract 16 first:
$2x = 50 - 16$
$2x = 34$
Divide by 2:
$x = \frac{34}{2}$
$x = 17$

Answer:

a. $x = 32$
b. $x$
c. $x = 17$