Expand menu menu_open Minimize Start chapters Home History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
menu_open
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open

Solving Multi-Step Equations

Solving Multi-Step Equations 1.14 - Solution

arrow_back Return to Solving Multi-Step Equations
a
To determine the number of possible solutions, we should solve the equation for r.r. Let's start with multiplying both sides by 3.3. This way, we get an equivalent equation without fractions.
2(4r+6)=23(12r+18)2(4r+6)=\dfrac{2}{3}(12r+18)
6(4r+6)=2(12r+18)6(4r+6)=2(12r+18)
24r+36=2(12r+18)24r+36=2(12r+18)
24r+36=24r+3624r+36=24r+36
Rewriting the equation resulted in the same expression on both sides. Thus, the equality holds true for all values of r.r. Therefore, the equation has infinitely many solutions.
b
On the left-hand side, we have a product of 55 and a parenthetical expression. To evaluate this product, we distribute 55 to each term in the parentheses. Then we can continue solving the equation.
n+5(n1)=7n+5(n-1)=7
n+5n5=7n+5n-5=7
6n5=76n-5=7
6n=126n=12
n=2n=2
Thus, the equation has one solution.
c
To solve this equation for y,y, we need to remember that when removing a negative parentheses we need to change signs on the terms inside. We will then combine like terms to isolate y.y.
8y(2y3)=128y-(2y-3)=12
8y2y+3=128y-2y+3=12
6y+3=126y+3=12
6y=96y=9
y=96y=\dfrac{9}{6}
The equation has one solution.