Solve the equation filling in the steps: 2(x−3)+21=−3

Question

(6 points)

Distribute to get Response area

Combine like terms to get Response area

Use the (choose a property) Response area to get (resulting equation) Response area

Use the (choose a property) Response area to get (resulting answer) Response area

The option "Division Property of Equality" (7 of 14) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.

Answer 1

Let's solve the equation step by step:

Given equation: \[ 2(x - 3) + 21 = -3 \]

Step 1: Distribute

We need to distribute the 2 across the terms inside the parentheses. \[ 2(x) - 2(3) + 21 = -3 \] This simplifies to: \[ 2x - 6 + 21 = -3 \]

Step 2: Combine like terms

Now, combine like terms on the left side: \[ 2x + ( -6 + 21 ) = -3 \] This simplifies to: \[ 2x + 15 = -3 \]

Step 3: Use the Subtraction Property of Equality

To isolate the term with x, we subtract 15 from both sides: \[ 2x + 15 - 15 = -3 - 15 \] This results in: \[ 2x = -18 \]

Step 4: Use the Division Property of Equality

Next, we divide both sides by 2 to solve for x: \[ \frac{2x}{2} = \frac{-18}{2} \] This simplifies to: \[ x = -9 \]

Final Answer

The solution to the equation is: \[ x = -9 \]