Question

linear equations w/ distribution (lev 2) score: 1/3 penalty: none question solve for x. $-5(-5x - 4) - 4x + 2 = 43$ answer attempt 1 out of 4 $x = $ input box submit answer watch video show examples

Explanation:

Step1: Distribute -5

First, we distribute the -5 into the parentheses \(-5(-5x - 4)\). Using the distributive property \(a(b + c)=ab+ac\), we get \((-5)\times(-5x)+(-5)\times(-4)=25x + 20\). So the equation becomes \(25x + 20-4x + 2 = 43\).

Step2: Combine like terms

Next, we combine the \(x\)-terms and the constant terms. For the \(x\)-terms: \(25x-4x = 21x\). For the constant terms: \(20 + 2=22\). So the equation simplifies to \(21x+22 = 43\).

Step3: Subtract 22 from both sides

We subtract 22 from both sides of the equation to isolate the term with \(x\). So \(21x+22-22 = 43-22\), which simplifies to \(21x=21\).

Step4: Divide by 21

Finally, we divide both sides of the equation by 21 to solve for \(x\). So \(\frac{21x}{21}=\frac{21}{21}\), which gives \(x = 1\).

Answer:

\(x = 1\)