SIMPLIFY IT
Simplify: 5x + 8x
13x
Solve: 3x + 7 = 22
x = 5
Solve: 5x + 2 = 2x + 17
x=5
A student says 3(x + 4) = 3x + 4. What is the mistake?
The 3 must multiply both terms: 3x + 12.
A club charges $12 to join and $5 per visit. Write the cost for v visits.
12 + 5v dollars
Simplify: 9a − 4a + 6
5a+6
Solve: 4(y − 2) = 28
y = 9
Solve: 8y − 3 = 5y + 12
Y=5
A student solves 5x − 7 = 18 and gets x = 2. Find the error.
Add 7 first: 5x = 25, so x = 5.
A $9 fee plus $4 per movie totals $33. How many movies?
6 movies
Simplify: 3(2m + 5)
6m + 15
Solve: 6m + 5 − 2m = 25
m= 5
Solve: 4(a + 2) = 2a + 18
a = 5
A student simplifies 8x − 3x + 2 as 5x² + 2. Correct it.
Subtract coefficients, not exponents: 5x + 2.
A rectangle has length 3x + 2 and width x. Simplify its perimeter.
8x + 4
Simplify: 4y + 2(y − 7)
6y - 14
Solve: 3(2n + 4) − 5 = 31
n = 4
Solve: 4(a + 2) = 2a + 18
No solution
A student solves 4(x − 2) = 20 and says x = 3. Explain the error.
4x − 8 = 20, so 4x = 28 and x = 7.
Plan A costs 18 + 3m dollars; Plan B costs 6 + 5m. When are costs equal?
m = 6
Simplify: 5(2p − 3) − 3p + 8
7p − 7
Solve: 5(2p − 3) + 7 = 42
P= 5
Classify: 3(2m + 1) = 6m + 3
Many solutions
A student says 6x + 4 = 6x − 2 has x = −6. What is the correct classification?
No solution: subtracting 6x gives 4 = −2, a false statement
A bike rental costs $14 plus $7 per hour. A customer pays $63. How many hours?
7 hours: 14 + 7h = 63, so h = 7.
A student claims x = 5 solves 4(2x − 3) + 5 = 3x + 18. Is the claim correct? Solve and check.
Yes. 8x − 7 = 3x + 18, so 5x = 25 and x = 5. Check: 33 = 33.