Question

1. 5.5(2x + 1) = -5.5x + 63.25

Explanation:

Problem 5: Solve \(-9.5(2x - 10) = 3.6(-6x + 26)\)

Step 1: Distribute both sides

First, we distribute \(-9.5\) on the left side and \(3.6\) on the right side.
For the left side: \(-9.5\times2x=-19x\) and \(-9.5\times(-10) = 95\), so the left side becomes \(-19x + 95\).
For the right side: \(3.6\times(-6x)=-21.6x\) and \(3.6\times26 = 93.6\), so the right side becomes \(-21.6x + 93.6\).
Now our equation is: \(-19x + 95=-21.6x + 93.6\)

Step 2: Add \(21.6x\) to both sides

To get all the \(x\) terms on one side, we add \(21.6x\) to both sides.
\(-19x+21.6x + 95=-21.6x+21.6x + 93.6\)
Simplifying, we have \(2.6x+95 = 93.6\)

Step 3: Subtract 95 from both sides

Now we subtract 95 from both sides to isolate the term with \(x\).
\(2.6x+95 - 95=93.6 - 95\)
Simplifying, we get \(2.6x=-1.4\)

Step 4: Divide both sides by 2.6

To solve for \(x\), we divide both sides by \(2.6\).
\(x=\frac{-1.4}{2.6}\)
We can multiply numerator and denominator by 10 to eliminate decimals: \(x=\frac{-14}{26}\), and simplifying the fraction (dividing numerator and denominator by 2) gives \(x =-\frac{7}{13}\approx - 0.538\)

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

Step 1: Distribute the left side

We distribute \(5.5\) on the left side.
\(5.5\times2x = 11x\) and \(5.5\times1=5.5\), so the left side becomes \(11x + 5.5\)
Now our 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.
\(11x+5.5x + 5.5=-5.5x+5.5x + 63.25\)
Simplifying, we have \(16.5x+5.5 = 63.25\)

Step 3: Subtract 5.5 from both sides

Now we subtract 5.5 from both sides to isolate the term with \(x\).
\(16.5x+5.5 - 5.5=63.25 - 5.5\)
Simplifying, we get \(16.5x = 57.75\)

Step 4: Divide both sides by 16.5

To solve for \(x\), we divide both sides by \(16.5\).
\(x=\frac{57.75}{16.5}\)
Calculating the division, we get \(x = 3.5\)

Answer:

s:
Problem 5: \(x =-\frac{7}{13}\) (or approximately \(-0.54\))
Problem 6: \(x = 3.5\)