Two-Step Equations
Write the equation to represent "Five more than twice a number is 15." Solve it.
Answers may vary.
5+2x=15
Solve: 2(x + 3) = 14.
x=4
Simplify: 3(x + 4).
3x+12
What is a unique solution in an equation?
A unique solution in an equation is when there is only one possible value for the variable that makes the equation true.
A rectangle's length is twice its width. If the perimeter is 24, write and solve for the width.
w=4
Solve the equation: 3x - 7 = 8.
x=5
What is x if 3(x - 2) + 4 = 10?
x=4
Apply the distributive property to 5(2x + 3) and simplify.
10x+15
Describe what it means for an equation to have no solution with an example.
An equation has no solution if there is no value for the variable that makes the equation true.
If you save $50 a month, how many months will it take to save $300? Write the equation and solve.
50m=300
m=6If 2x + 5 = 17, what is the value of x?
x=6
Solve the equation: 4x - 5 = 3x + 2.
x=7
Expand and simplify: 2(3x - 5) + 4.
6x-6
If an equation results in a true statement like 0 = 0, what type of solution does it have?
Infinity many solutions.
A car's value decreases by 15% each year. If it’s worth $20,000 now, how much will it be worth in one year? Write the equation and solve.
Equations may vary.
Ex: c=0.85(20,000) or c=20,000-20,000(0.15)
c=17,000
Write and solve the equation for "The sum of a number and 12 equals 30."
x+12=30
x=18If 5(2x - 1) = 20, what is x?
x=2.5
Distribute and simplify: 7(x + 2) - 3(x - 4).
4x-26
Give an example of an equation with infinitely many solutions.
Answers may vary.
Write and solve an equation for a situation where a student has $30 and spends $5 each week. How many weeks can they spend before running out?
Equations may vary.
Ex. 30-5w=0
w=6A number decreased by 4 equals 10. Write the equation and find the number.
w-4=10
w=14
Solve: 6 - 2(3x - 4) = 10.
x=2/3
If 4(a + 2) = 28, what is a?
a=5
Explain how you would determine the type of solution for the equation 2x + 6 = 2(x + 3).
Answers may vary. After distributing the 2 on the right side of the equation you have 2x+6=2x+6. If both side of the equation are the same then there are infinitely many solutions.
If a concert ticket costs $45 and you have $200, how many tickets can you buy? Write and solve the equation.
45x=200
x=4.444 (repeating)
You can buy 4 tickets with 20 dollars left over for a drink (and maybe a pretzel).