directions: solve the following equations. 1) 7x - 4 = 2x + 11 2) 10 + 3x = 6x - 2 3) 2(x + 4) = 3x - 2

Explanation:

Step1: Move x - terms to one side

Subtract 2x from both sides of 7x - 4 = 2x + 11: $7x-2x - 4=2x-2x + 11$ $5x-4 = 11$

Step2: Isolate the term with x

Add 4 to both sides: $5x-4 + 4=11 + 4$ $5x=15$

Step3: Solve for x

Divide both sides by 5: $\frac{5x}{5}=\frac{15}{5}$ $x = 3$

For equation 2) 10 + 3x = 6x - 2

Step1: Move x - terms to one side

Subtract 3x from both sides: $10+3x-3x=6x-3x - 2$ $10 = 3x-2$

Step2: Isolate the term with x

Add 2 to both sides: $10 + 2=3x-2 + 2$ $12 = 3x$

Step3: Solve for x

Divide both sides by 3: $\frac{12}{3}=\frac{3x}{3}$ $x = 4$

For equation 3) 2(x + 4)=3x - 2

Step1: Expand the left - hand side

Use the distributive property: $2x+8 = 3x-2$

Step2: Move x - terms to one side

Subtract 2x from both sides: $2x-2x+8=3x-2x - 2$ $8=x - 2$

Step3: Solve for x

Add 2 to both sides: $8 + 2=x-2 + 2$ $x = 10$

Answer:

1. $x = 3$
2. $x = 4$
3. $x = 10$