Question

lessons 2 - 4 and 2 - 5 write two - step equations | solve two - step equations
quick review
equations can be used to represent situations. two - step equations have two different operations. the properties of equality can be applied the same way when solving two - step equations as when solving one - step equations.
example
there are red and yellow flowers in a city park. the number of yellow flowers is 3 more than 1/3 of the number of red flowers. there are 21 yellow flowers. write an equation to find the number of red flowers. let r represent the number of red flowers. then solve for r.
1/3r + 3 = 21
1/3r + 3 - 3 = 21 - 3
1/3r = 18
(3)1/3r = 18(3)
r = 54
the garden has 54 red flowers.
practice

1. the total number of students in the seventh grade is 9 more than 4 times as many students as are in the art class. there are 101 students in the seventh grade. write and solve an equation to find the number of students in the art class. let x represent the number of students in the art class.
2. list the steps to solve the following equation: 5x - 6 = 44. then solve for x.
3. solve for the given variable.

a. 4y + 3 = 19
b. 1/2n - 3 = 5
lesson 2 - 6 solve equations using the distributive property
quick review
use the distributive property to solve problems of the form p(x + q)=r.
example
solve the equation 2(4.3 + n)=17.63.
8.6 + 2n = 17.63
2n = 9.03
n = 4.515
practice

1. there are 450 seats in the lower level of a concert hall with b balcony seats in the upper level. so far, 170 tickets have been sold, which is 1/5 of the total number of seats in the concert hall. how many tickets sold are balcony seats?
2. solve the equation - 4(8 + y)=90.

Explanation:

1.

Step1: Translate the situation into an equation

Let $x$ be the number of students in the art - class. The number of seventh - grade students is 9 more than 4 times the number of students in the art class, so the equation is $4x + 9=101$.

Step2: Solve the equation for $x$

Subtract 9 from both sides: $4x+9 - 9=101 - 9$, which simplifies to $4x = 92$. Then divide both sides by 4: $\frac{4x}{4}=\frac{92}{4}$, so $x = 23$.

Step1: Add 6 to both sides

To isolate the term with $x$, add 6 to both sides of the equation $5x−6 = 44$. We get $5x-6 + 6=44 + 6$, which simplifies to $5x = 50$.

Step2: Divide both sides by 5

Divide both sides of the equation $5x = 50$ by 5. So, $\frac{5x}{5}=\frac{50}{5}$, and $x = 10$.

Step1: Subtract 3 from both sides

For the equation $4y + 3=19$, subtract 3 from both sides: $4y+3 - 3=19 - 3$, which gives $4y = 16$.

Step2: Divide both sides by 4

Divide both sides of $4y = 16$ by 4: $\frac{4y}{4}=\frac{16}{4}$, so $y = 4$.

Answer:

There are 23 students in the art class.

2.