Download 1) 7 - 8x = 4x -17

Steps for Solving Linear Equations with Variables on Both Sides
1. Use the distributive property to remove any grouping symbols.
2. Simplify the expression on each side of the equation by combining like terms.
3. Use property of equality to collect the variable terms on one side of the equal sign
and constants on the other.
4. Solve for the variable.
5. Check your solution.
Side to collect terms with x
1)
7 - 8x = 4x -17
+8x
+8x
7
= 12x – 17
+17
+17
24 = 12x
X=2
3)
9 - 3k = 17 - 2k
5) 9x - 5 = 1 (16x + 60)
4
2) - 5(a - 1) = -6a + 11
-5a + 5 = -6a + 11
+6a
+6a
1a + 5 = 11
-5 -5
a=6
4) 5z - 2 = 2(3z - 4)
6) 8y - 6 = (6y +15)
8y – 6 = (6y) + (15)
8y – 6 = 4y + 10
-4y
-4y
4y – 6 = 10
4y = 16
Y=4
7) 3x = 3(x + 4)
8) 2x + 10 = 2(x+ 5)
-Simplify
9) A car dealership sold 78 new cars and 67 used cars this year. The number of new
cars sold by the dealership has been increasing by 6 cars each year. The number of
used cars sold by the dealership has been decreasing by 4 cars each year. If these
trends continue, in how many years will the number of new cars sold be twice the
number of used cars sold?
Let x = years,
# of new cars = 2 · ( # of old cars)
78 + 6x = 2( 67 – 4x)
78 + 6x = 134 – 8x
78 + 14x = 134
14x = 56
Answer: in 4 years
X=4
10) A music web site sold 94 single songs and 67 albums today. The number of single
downloads has been increasing by 22 each day. The number of album downloads has
been decreasing by 5 each day. If these trends continue, in how many days will the
number of single downloads be ten times the number of album downloads?
Let x = # of days
94 + 22x = 10(67 – 5x)
94 + 22x = 670 - 50x
+50x
+ 50x
94 + 72x = 670
72x = 576
X=8
11) Find the perimeter of the square:
5x = 3x + 6
-3x -3x
It is a square!
2x = 6
X = 3 This is not the answer yet!
If x = 3, then each side must be: 5(3) = 15
Now we can find the perimeter: 15 · 4 = 60
12) The membership fee for joining a camping association is $45. A local campground
charges members of the camping association $35 per night for a campsite and
nonmembers $40 per night for a campsite. After how many nights of camping is the total
cost for members, including the membership fee, the same as the total cost for
nonmembers?
Let x = nights
Then members are paying 35x total for all their nights, plus one-time fee of $45
And non-members are paying 40x total:
35x + 45 = 40x
-35x
-35x
45 = 5x
x=9
Answer: break-even point is in 9 nights