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)

Options for the response areas: 2x - 6 + 21 = -3, 2x = -21, x = - 21/2, Subtraction Property of Equality, Multiplication Property of Equality, x = 24, 2x + 15 = -3, 2x = -18, Addition Property of Equality, 2x - 3 + 21 = -3, x = -9, -1x = -24, Division Property of Equality, 2x + 18 = -3

Answer 1

Let's solve the equation step by step.

Step 1: Distribute to get \[ 2(x - 3) + 21 = -3 \] Distributing the 2 we get: \[ 2x - 6 + 21 = -3 \]

Step 2: Combine like terms to get \[ 2x - 6 + 21 = -3 \] Combining \(-6 + 21\) gives us: \[ 2x + 15 = -3 \]

Step 3: Use the (choose a property) to get resulting equation (Response area) We will use the Subtraction Property of Equality to isolate the term with \(x\): \[ 2x + 15 - 15 = -3 - 15 \] This simplifies to: \[ 2x = -18 \]

Step 4: Use the (choose a property) to get resulting answer (Response area) Now we will use the Division Property of Equality to solve for \(x\): \[ \frac{2x}{2} = \frac{-18}{2} \] This simplifies to: \[ x = -9 \]

So the solution is: \[ \boxed{-9} \]