Question

solve for x.
-5(-5x + 2) + 3x + 5 = 23

Explanation:

Step1: Distribute the -5

First, we distribute the -5 across the terms inside the parentheses \(-5(-5x + 2)\). Using the distributive property \(a(b + c)=ab+ac\), we get \((-5)\times(-5x)+(-5)\times2 = 25x-10\). So the equation becomes \(25x - 10+3x + 5 = 23\).

Step2: Combine like terms

Next, we combine the like terms. For the \(x\)-terms: \(25x+3x = 28x\). For the constant terms: \(-10 + 5=-5\). So the equation simplifies to \(28x-5 = 23\).

Step3: Add 5 to both sides

We add 5 to both sides of the equation to isolate the term with \(x\). So \(28x-5 + 5=23 + 5\), which simplifies to \(28x=28\).

Step4: Divide by 28

Finally, we divide both sides by 28 to solve for \(x\). \(\frac{28x}{28}=\frac{28}{28}\), so \(x = 1\).

Answer:

\(x = 1\)