Question

simplify one side first

1. ( 3 ( x + 2 ) = 2 x + 14 )
2. ( 5 ( y - 4 ) + 2 = 3 y - 6 )
3. ( 2 ( n + 5 ) + n = 4 n + 3 )
4. ( 4 ( x - 1 ) + 3 = 2 x + 5 )
5. ( 6 m + 4 + 2 m = 3 m + 19 )

distribution on both sides

1. ( 2 ( x + 3 ) = 3 ( x - 1 ) )
2. ( 4 ( y - 2 ) + 5 = 2 ( y + 6 ) )
3. ( 3 ( n - 4 ) = 2 ( n + 1 ) + 5 )
4. ( 2 ( x + 5 ) - 3 = 3 ( x - 1 ) + 4 )
5. ( 5 ( 2 m - 1 ) = 3 ( m + 7 ) - m )

word problems

1. competing streaming plans

• plan a charges $10 per month plus $4 per movie.
• plan b charges $6 per month plus $5 per movie.

after how many movies will the total monthly cost be the same?

1. two lawn services

• service a charges $25 per visit plus $15 per hour of mowing.
• service b charges $40 per visit plus $10 per hour.

after how many hours will the total costs be equal?

1. equal sides, different expressions

• two sides of a trapezoid are equal in length.
• the first side measures ( 4 x + 3 mathrm { cm } ).
• the second side measures ( 2 ( x + 6 ) mathrm { cm } ).

find the value of ( x ) that makes the sides equal.

Explanation:

Step1: Expandir la ecuación

$$4x + 3=2(x + 6)$$
$$4x + 3=2x+12$$

Step2: Mover términos con \(x\) al lado izquierdo y constantes al derecho

$$4x-2x=12 - 3$$
$$2x=9$$

Step3: Resolver para \(x\)

$$x=\frac{9}{2}=4.5$$

Answer:

\(x = 4.5\)