8-1 Solving Equations with Rational Coefficients
9x = 5.4
0.6
4p+9 = 25
4
Solve the problem by writing and solving an equation
Kendra pays $132 for shoes and clothes. The clothes cost $54 more than the shoes. How much do the shoes cost?
Equation: 2s+54=132
Answer: $39
2x+3=x
x=-3
What is the solution to the equation -6.5x = 59.8?
x = -9.2
-25/36 = -5/6 r
5/6
-7-8d=17
-3
During the spring car wash, the Activities Club washed 14 fewer cars than during the summer car wash. They washed a total of 96 cars during both car washes. How many cars did they wash during the spring car wash?
Equation: 2x-14 = 96
Answer: 41 cars
5.3x+2-4.1x=3.6x-1.6
1.5
Solve 0.5(8x - 12) = -10.
x = -1
5p-2p = -12
-4
The second book in a fantasy series is 112 pages longer than the first book. The total number of pages in both books is 524. Solve the equation b+b+112 =524 to find the number of pages b in the first book
206 pages
Eileen drove for 85 minutes. This is 21 more minutes than one-third the number of minutes Ethan drove.
1/3n + 21 = 85
4/5c-1/10c=9/10c
0
An artist creates 9 identical ceramic vases. Each vase contains some clay and 1.5 pounds of glass. The artist uses a total of 49.5 pounds of clay and glass to make the vases. Each vase contains how many pounds of clay?
4 pounds
If 3/10x = 3, what is the value of 7x+13?
83
Tenisha bought some gel pens that cost $1.29 each. She also bought a notebook for $3.59. She spent a total of $10.04 on these items. Solve the equation 1.29g+3.59-10.04 to find the number of gel pens she bought.
5
Emelia discovered that if she takes three-fourths of her age and adds 9, it produces the same result as when she takes one-fourth of her age and adds 21. How old is Emelia?
24 years old
Mykia is solving the equation 10x + 6 = 8x - 4. Find her mistake and correct it.
10x + 6 = 8x - 4
10x -10x + 6 = 8x - 4 - 10 x
6 = 4 - 2x
2 = -2x
-1 = x
In the third step, the 4 should be negative, not a positive. The correct solution is x = -5
A car sales associate receives a monthly salary of $1,700 a month plus $140 for every car he sells. How many cars must he sell monthly to earn at least $4,500?
at least 20 cars
Sam is solving 1/4x = -20. Find his mistake and correct it
1/4x ÷ 4 = -20 ÷ 4
x = -5
He should have multiplied each side by 4, so x = -80
54.8- 1/5d = 60.1
-26.5
An example of two consecutive even numbers is 4 and 6. They can be represented by n and n + 2. Find 3 consecutive even numbers whose sum is 30.
8,10,12
The cost of a tank of gas at $4.18 per gallon was at most $58. Which inequality can be used to find out how many gallons of gas were purchased?
F. 4.18g < 58
H. 4.18g > 58
G. 4.18g ≥ 58
J. 4.18g ≤ 58
J
The sum of an integer and the next greater integer is at most 13. Write an inequality to find the lesser integer. Then solve for the lesser integer.
equation: n+n+1≤13
answer: n ≤ 6