Q45. - Algebra 1

Question

REASONING Determine whether each solution is correct. If the solution is not correct, describe the error and give the correct solution.

a. 

$\begin{array}{l}2\left(g+5\right)=22\\ 2g+5=22\\ 2g+5-5=22\\ 2g=17\\ 2g=8.5\end{array}$

b. 

$\begin{array}{l}5d=2d-18\\ 5d-2d=2d-18-2d\\ 3d=-18\\ d=-6\end{array}$

c.

$\begin{array}{l}-6z+13=7z\\ -6z+13-6z=7z-6z\\ 13=z\end{array}$

Step-by-Step Solution

Answer

a. The given solution is incorrect. The correct solution is $g=6$.

b. The given solution is correct.

c. The given solution is incorrect. The correct solution is $z=1$.

Part a. Step 1. State the concept.

An equation is solved by using the same operation on both sides of the equals sign and thus isolating the variable on one side and its value on the other side.

Part a. Step 2. List the given data.

$\begin{array}{l}2\left(g+5\right)=22\\ 2g+5=22\\ 2g+5-5=22\\ 2g=17\\ 2g=8.5\end{array}$

Part a. Step 3. Determine if the given solution is correct.

The given solution is incorrect because, in the first step, 2 should also be multiplied by 5, in the third step, 5 should be subtracted from both sides and in the last step, 2 should be divided from both sides.

Part a. Step 4. Write the correct solution.

$\begin{array}{l}2\left(g+5\right)=22\\ 2g+10=22\\ 2g+10-10=22-10\\ 2g=12\\ g=6\end{array}$

This is the correct solution.

Part b. Step 1. State the concept.

An equation is solved by using the same operation on both sides of the equals sign and thus isolating the variable on one side and its value on the other side.

Part b. Step 2. List the given data.

$\begin{array}{l}5d=2d-18\\ 5d-2d=2d-18-2d\\ 3d=-18\\ d=-6\end{array}$

Part b. Step 3. Determine if the given solution is correct.

The given solution is correct because, in all the steps, the required operations have been carried out on both sides of the equation.

Part c. Step 1. State the concept.

An equation is solved by using the same operation on both sides of the equals sign and thus isolating the variable on one side and its value on the other side.

Part c. Step 2. List the given data.

$\begin{array}{l}-6z+13=7z\\ -6z+13-6z=7z-6z\\ 13=z\end{array}$

Part c. Step 3. Determine if the given solution is correct.

The given solution is incorrect because in the second step, should be added, not subtracted.

Part c. Step 4. Write the correct solution.

$\begin{array}{l}-6z+13=7z\\ -6z+13+6z=7z+6z\\ 13=13z\\ 1=z\end{array}$

This is the correct solution.