Complete the table by filling in the missing algebraic steps...

Complete the table by filling in the missing algebraic steps to solve the equation or supply the missing reasons for those steps. $$ 2(x-5)+7=-3 x+12 $$ $$ \begin{array}{|c|l|} \hline \begin{array}{c} \text { Algebraic Step to Solve the } \\ \text { Equation } \end{array} & {\text { Reason for Each Step }} \\ \hline 2(x-5)+7=-3 x+12 & \\ 2 x-10+7=-3 x+12 & \\ \hline & \begin{array}{l} \text { Combine like terms on each } \\ \text { side of the equation. } \end{array} \\ \hline \begin{array}{c} 2 x-3=-3 x+12 \\ +3 x & +3 x \end{array} & \\ \hline & \begin{array}{l} \text { Isolate the variable term using } \\ \text { the addition property of equality. } \end{array} \\ \hline & \begin{array}{l} \text { Solve for the variable using the } \\ \text { division property of equality. } \end{array} \\ \hline x=3 & \\ \hline \end{array} $$

Complete the table by filling in the missing algebraic steps to solve the equation or supply the missing reasons for those steps.
$$
2(x-5)+7=-3 x+12
$$
$$
\begin{array}{|c|l|}
\hline \begin{array}{c}
\text { Algebraic Step to Solve the } \\
\text { Equation }
\end{array} & {\text { Reason for Each Step }} \\
\hline 2(x-5)+7=-3 x+12 & \\
2 x-10+7=-3 x+12 & \\
\hline & \begin{array}{l}
\text { Combine like terms on each } \\
\text { side of the equation. }
\end{array} \\
\hline \begin{array}{c}
2 x-3=-3 x+12 \\
+3 x & +3 x
\end{array} & \\
\hline & \begin{array}{l}
\text { Isolate the variable term using } \\
\text { the addition property of equality. }
\end{array} \\
\hline & \begin{array}{l}
\text { Solve for the variable using the } \\
\text { division property of equality. }
\end{array} \\
\hline x=3 & \\
\hline
\end{array}
$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Isolating the Variable

The process of rearranging an equation so that the variable of interest stands alone on one side. This often involves combining like terms, moving terms using addition or subtraction, and finally using division or multiplication to solve for the variable.

Division Property of Equality

An algebraic property which asserts that dividing both sides of an equation by the same nonzero number maintains equality. This is crucial for isolating the variable after applying previous simplification steps.

Combining Like Terms

A simplification process in which terms that contain the same variables and exponents are merged into a single term by adding or subtracting their coefficients. This step reduces the complexity of equations and prepares them for further manipulation.

Distributive Property

A fundamental property used to expand expressions by multiplying a single term by each term within parentheses. It allows the transformation of expressions like a(b + c) into ab + ac, which is essential for simplifying equations.

Addition Property of Equality

A basic principle in algebra stating that if two expressions are equal, the same quantity can be added to both sides of the equation without affecting the balance of the equation. This property is often used to isolate variable terms.

Transcript

Please give Ace some feedback