Two-Step Equations
Solve: 2x + 4 = 16
x = 6
Solve: 3(x + 2) = 21
x = 5
2x + 3 = x + 11
x = 8
A student solved: x + 6 = 10
x = 16
What mistake was made?
The student added 6 instead of subtracting 6.
A movie ticket costs $12. You have $48. How many tickets can you buy?
Must show the equations AND the answer!
Equation: 12x = 48
x = 4 tickets
Solve: 3x − 5 = 16
x = 7
Solve: 2(x − 4) + 6 = 18
x = 10
Solve: 5x − 4 = 2x + 11
x = 5
A student solved: 3x = 18
x = 15
What mistake was made?
The student divided incorrectly. 18 ÷ 3 = 6.
A gym charges a $10 fee plus $15 per month. Your total is $70.
Must show the equation AND the answer!
Equation: 15x + 10 = 70
x = 4 months
Solve: x/4 + 3 = 8
x = 20
Solve: 4[2x + 1] − 8 = 24
x = 3.5
Solve: 7x + 2 = 4x + 20
x = 6
A student solved: 2(x + 4) = 10
2x + 4 = 10
What mistake was made?
The student did not distribute the 2 to both terms.
A streaming service charges a $12 sign-up fee plus $5 per month. Another service charges $3 per month plus a $20 sign-up fee. After how many months will the costs be the same?
Must show the equation AND the answer!
Equation: 5x + 12 = 3x + 20
x = 4 months
Solve: 5x + 7 = 42
x = 7
Solve: 3(2x − 5) + 4 = 19
x = 5
9x − 5 = 3x + 19
x = 4
A student solved: 5x − 2 = 3x + 8
2x − 2 = 8
What mistake was made?
The equation setup is incomplete. The student still needs to add 2 to both sides and solve.
A school fundraiser sells shirts online and in person. Online sales earn $8 per shirt plus a $30 bonus. In-person sales earn $10 per shirt plus a $10 bonus. How many shirts sold will make the profits equal?
Must show the equation AND the answer!
Equation: 8x + 30 = 10x + 10
x = 10 shirts
Solve: −2x + 9 = 21
x = -6
Solve: 2[3(x − 1) + 4] = 20
x = 3
Solve: 4(x − 2) = 2x + 8
x = 8
A student solved: 4x + 6 = 4x − 3
x = −9
What mistake was made?
The variables cancel out, leaving 6 = −3, which is false. The equation has no solution.
The same four friends buy tickets for two shows on consecutive nights. They use a coupon for $5 off each ticket. They pay a total of $416 for 8 tickets. Find the original price of the tickets.
Must show the equation AND the answer!
Equation: 8(x - 5) = 416
x = 57