Question

practice
model and solve each equation using algebra tiles.

1. $3x + 6 = -2x - 4$ $x = \underline{\quad\quad}$
2. $-x + 6 = -3x + 2$ $x = \underline{\quad\quad}$

solve each equation.

1. $5x + 15 = 75 - 25x$ $x=\underline{\quad\quad}$
2. $11.3x + 12.8 = 7.5x + 35.6$ $x=\underline{\quad\quad}$
3. $\frac{1}{4}x - 3 = \frac{1}{2}x + 12$ $x = \underline{\quad\quad}$
4. $9.6x - 15.4 = -4.3x + 26.3$ $x = \underline{\quad\quad}$

Explanation:

Problem 1: \( 3x + 6 = -2x - 4 \)

Step1: Add \( 2x \) to both sides

\( 3x + 2x + 6 = -2x + 2x - 4 \)
\( 5x + 6 = -4 \)

Step2: Subtract 6 from both sides

\( 5x + 6 - 6 = -4 - 6 \)
\( 5x = -10 \)

Step3: Divide by 5

\( \frac{5x}{5} = \frac{-10}{5} \)
\( x = -2 \)

Step1: Add \( 3x \) to both sides

\( -x + 3x + 6 = -3x + 3x + 2 \)
\( 2x + 6 = 2 \)

Step2: Subtract 6 from both sides

\( 2x + 6 - 6 = 2 - 6 \)
\( 2x = -4 \)

Step3: Divide by 2

\( \frac{2x}{2} = \frac{-4}{2} \)
\( x = -2 \)

Step1: Add \( 25x \) to both sides

\( 5x + 25x + 15 = 75 - 25x + 25x \)
\( 30x + 15 = 75 \)

Step2: Subtract 15 from both sides

\( 30x + 15 - 15 = 75 - 15 \)
\( 30x = 60 \)

Step3: Divide by 30

\( \frac{30x}{30} = \frac{60}{30} \)
\( x = 2 \)

Answer:

\( x = -2 \)

Problem 2: \( -x + 6 = -3x + 2 \)