Question

directions: solve each equation. use your answer to find the color. use the color on the corres
1.
$3 - (-21x - 21) = 8(x + 5) + 10$
2.
$2(\frac{1}{5}x - 5) + \frac{3}{5}x = 9(\frac{1}{10}x - 1)$
$x = -2$ $x = 2$ $x = 13$ $x = 10$ $x = 1$ $x = \frac{1}{10}$
red green purple red green white

Explanation:

Problem 1:

Step 1: Simplify both sides

Simplify the left side: \(3 - (-21x - 21)=3 + 21x + 21 = 21x + 24\)
Simplify the right side: \(8(x + 5)+10 = 8x + 40 + 10 = 8x + 50\)
Now the equation is \(21x + 24 = 8x + 50\)

Step 2: Subtract \(8x\) from both sides

\(21x - 8x + 24 = 8x - 8x + 50\)
\(13x + 24 = 50\)

Step 3: Subtract 24 from both sides

\(13x + 24 - 24 = 50 - 24\)
\(13x = 26\)

Step 4: Divide by 13

\(\frac{13x}{13}=\frac{26}{13}\)
\(x = 2\)

Step 1: Distribute on both sides

Left side: \(2(\frac{1}{5}x - 5)+\frac{3}{5}x=\frac{2}{5}x - 10+\frac{3}{5}x=\frac{5}{5}x - 10 = x - 10\)
Right side: \(9(\frac{1}{10}x - 1)=\frac{9}{10}x - 9\)
Now the equation is \(x - 10=\frac{9}{10}x - 9\)

Step 2: Subtract \(\frac{9}{10}x\) from both sides

\(x - \frac{9}{10}x - 10=\frac{9}{10}x - \frac{9}{10}x - 9\)
\(\frac{1}{10}x - 10 = -9\)

Step 3: Add 10 to both sides

\(\frac{1}{10}x - 10 + 10 = -9 + 10\)
\(\frac{1}{10}x = 1\)

Step 4: Multiply by 10

\(10\times\frac{1}{10}x = 1\times10\)
\(x = 10\)

Answer:

\(x = 2\) (corresponding color: green)

Problem 2: