Question

linear equations w/ distribution (lev 2)
question
solve for x.
2(3x + 2) + 4x + 3 = -43
answer
x =
submit answer

Explanation:

Step1: Distribute the 2

First, we apply the distributive property to \(2(3x + 2)\). The distributive property states that \(a(b + c)=ab+ac\), so here \(a = 2\), \(b = 3x\), and \(c = 2\).

$$2(3x + 2)=2\times3x+2\times2 = 6x + 4$$

Now our equation becomes:

$$6x + 4+4x + 3=-43$$

Step2: Combine like terms

Next, we combine the \(x\)-terms (\(6x\) and \(4x\)) and the constant terms (\(4\) and \(3\)).
For the \(x\)-terms: \(6x+4x = 10x\)
For the constant terms: \(4 + 3=7\)
So the equation simplifies to:

$$10x+7=-43$$

Step3: Subtract 7 from both sides

We want to isolate the term with \(x\), so we subtract 7 from both sides of the equation.

$$10x+7 - 7=-43 - 7$$

Simplifying both sides:

$$10x=-50$$

Step4: Divide by 10

To solve for \(x\), we divide both sides of the equation by 10.

$$\frac{10x}{10}=\frac{-50}{10}$$

Simplifying gives:

$$x=-5$$

Answer:

\(x = - 5\)