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If -2(x-7)+(x-6)=23, find x...

If `-2(x-7)+(x-6)=23`, find x

A

`-31`

B

`-15`

C

`-5`

D

`-3`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the equation \(-2(x - 7) + (x - 6) = 23\), we will follow these steps: ### Step 1: Distribute the -2 We start by distributing \(-2\) to both terms inside the parentheses \((x - 7)\): \[ -2(x - 7) = -2x + 14 \] Now, we can rewrite the equation: \[ -2x + 14 + (x - 6) = 23 \] ### Step 2: Combine like terms Next, we combine the like terms on the left side of the equation: \[ -2x + x + 14 - 6 = 23 \] This simplifies to: \[ -x + 8 = 23 \] ### Step 3: Isolate the variable Now, we want to isolate \(-x\). We can do this by subtracting \(8\) from both sides: \[ -x = 23 - 8 \] This simplifies to: \[ -x = 15 \] ### Step 4: Solve for x To solve for \(x\), we multiply both sides by \(-1\): \[ x = -15 \] ### Final Answer Thus, the value of \(x\) is: \[ \boxed{-15} \] ---
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