Question

directions: you must show work for credit.
learning target: i can solve multi - step equations.

• goal when solving equations: isolate the variable.
• simplify each expression before solving (distributive property and combine like terms if needed)
• use inverse operations to cancel out values.
• keep the equation equal by performing the same operation to both sides of the equal sign.

1. $3x + 5 = 7x - 7$
2. $3m - 2 = 2m - 13$

a. $m = -11$
b. $m = 11$
c. $m = -15$
d. $m = 15$

1. $3(x - 5) = x + 1$

a. $x = 16$
b. $x = 8$
c. $x = 6$
d. $x = 3$

Explanation:

Problem 1: \( 3x + 5 = 7x - 7 \)

Step 1: Subtract \( 3x \) from both sides

To get all \( x \)-terms on one side, we subtract \( 3x \) from both sides. This gives:
\( 3x + 5 - 3x = 7x - 7 - 3x \)
Simplifying both sides:
\( 5 = 4x - 7 \)

Step 2: Add 7 to both sides

To isolate the term with \( x \), we add 7 to both sides:
\( 5 + 7 = 4x - 7 + 7 \)
Simplifying both sides:
\( 12 = 4x \)

Step 3: Divide by 4

To solve for \( x \), divide both sides by 4:
\( \frac{12}{4} = \frac{4x}{4} \)
Simplifying:
\( x = 3 \)

Step 1: Subtract \( 2m \) from both sides

To get all \( m \)-terms on one side, subtract \( 2m \) from both sides:
\( 3m - 2 - 2m = 2m - 13 - 2m \)
Simplifying:
\( m - 2 = -13 \)

Step 2: Add 2 to both sides

To isolate \( m \), add 2 to both sides:
\( m - 2 + 2 = -13 + 2 \)
Simplifying:
\( m = -11 \)

Step 1: Distribute the 3

Use the distributive property on the left side:
\( 3 \cdot x - 3 \cdot 5 = x + 1 \)
Simplifying:
\( 3x - 15 = x + 1 \)

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

To get all \( x \)-terms on one side, subtract \( x \) from both sides:
\( 3x - 15 - x = x + 1 - x \)
Simplifying:
\( 2x - 15 = 1 \)

Step 3: Add 15 to both sides

To isolate the term with \( x \), add 15 to both sides:
\( 2x - 15 + 15 = 1 + 15 \)
Simplifying:
\( 2x = 16 \)

Step 4: Divide by 2

To solve for \( x \), divide both sides by 2:
\( \frac{2x}{2} = \frac{16}{2} \)
Simplifying:
\( x = 8 \)

Answer:

\( x = 3 \)

Problem 2: \( 3m - 2 = 2m - 13 \)