Question

1. use the algebra tiles to write an equation. 2. solve the equation. $4x+10=3x+3$ $x=$ check your solution
2. use the algebra tiles to write an equation. 2. solve the equation. $2x+2=4x+20$ $x=$ check your solution
3. use the algebra tiles to write an equation. 2. solve the equation. $4x+(-5)=-1x+6$ $x=$ check your solution
4. use the algebra tiles to write an equation. 2. solve the equation. $10x+(-2)=-2x+4$ $x=$ check your solution
5. use the algebra tiles to write an equation. 2. solve the equation. $3x+9=2x+5$ $x=$ check your solution

Explanation:

Problem 6

Step1: Simplify the equation

Start with $4x + 10 = 3x + 3$
Subtract $3x$ from both sides:
$4x - 3x + 10 = 3x - 3x + 3$
$x + 10 = 3$

Step2: Isolate $x$

Subtract 10 from both sides:
$x + 10 - 10 = 3 - 10$
$x = -7$

Problem 7

Step1: Simplify the equation

Start with $2x + 2 = 4x + 20$
Subtract $2x$ from both sides:
$2x - 2x + 2 = 4x - 2x + 20$
$2 = 2x + 20$

Step2: Isolate the $x$-term

Subtract 20 from both sides:
$2 - 20 = 2x + 20 - 20$
$-18 = 2x$

Step3: Solve for $x$

Divide by 2:
$x = \frac{-18}{2} = -9$

Problem 8

Step1: Simplify the equation

Start with $4x - 5 = -x + 10$
Add $x$ to both sides:
$4x + x - 5 = -x + x + 10$
$5x - 5 = 10$

Step2: Isolate the $x$-term

Add 5 to both sides:
$5x - 5 + 5 = 10 + 5$
$5x = 15$

Step3: Solve for $x$

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

Problem 9

Step1: Simplify the equation

Start with $9x - 2 = -2x + 4$
Add $2x$ to both sides:
$9x + 2x - 2 = -2x + 2x + 4$
$11x - 2 = 4$

Step2: Isolate the $x$-term

Add 2 to both sides:
$11x - 2 + 2 = 4 + 2$
$11x = 6$

Step3: Solve for $x$

Divide by 11:
$x = \frac{6}{11}$

Problem 10

Step1: Simplify the equation

Start with $3x + 9 = 2x + 5$
Subtract $2x$ from both sides:
$3x - 2x + 9 = 2x - 2x + 5$
$x + 9 = 5$

Step2: Isolate $x$

Subtract 9 from both sides:
$x + 9 - 9 = 5 - 9$
$x = -4$

Answer:

Problem 6: $x = -7$
Problem 7: $x = -9$
Problem 8: $x = 3$
Problem 9: $x = \frac{6}{11}$
Problem 10: $x = -4$