Question

1. -9.5(2x - 10) = 3.8(-5x + 25)
2. 5.5(2x + 1) = -5.5x + 63.25

square and equilateral triangle below
al perimeters. find the value of x.
culate the perimeter of each shap

Explanation:

Problem 3: Solve \(-9.5(2x - 10) = 3.8(-5x + 25)\)

Step 1: Distribute both sides

First, we use the distributive property \(a(b + c)=ab+ac\) on both sides of the equation.
For the left side: \(-9.5\times2x+(-9.5)\times(-10)=-19x + 95\)
For the right side: \(3.8\times(-5x)+3.8\times25=-19x + 95\)
So the equation becomes \(-19x + 95=-19x + 95\)

Step 2: Analyze the equation

We can see that if we add \(19x\) to both sides, we get \(95 = 95\). This is a true statement for all real numbers \(x\).

Step 1: Distribute the left side

Using the distributive property \(a(b + c)=ab + ac\) on the left side:
\(5.5\times2x+5.5\times1 = 11x+5.5\)
So the equation is \(11x + 5.5=-5.5x+63.25\)

Step 2: Add \(5.5x\) to both sides

To get all the \(x\) terms on one side, we add \(5.5x\) to both sides:
\(11x+5.5x + 5.5=-5.5x+5.5x + 63.25\)
\(16.5x+5.5 = 63.25\)

Step 3: Subtract \(5.5\) from both sides

Subtract \(5.5\) from both sides to isolate the term with \(x\):
\(16.5x+5.5 - 5.5=63.25 - 5.5\)
\(16.5x=57.75\)

Step 4: Divide both sides by \(16.5\)

Divide both sides by \(16.5\) to solve for \(x\):
\(x=\frac{57.75}{16.5}\)
\(x = 3.5\) (or \(\frac{7}{2}\))

Answer:

All real numbers (or \(x\in\mathbb{R}\))

Problem 6: Solve \(5.5(2x + 1)=-5.5x + 63.25\)