Equations
3p + 8 = 35
p=9
x + 7 > 15
x > 8
If you add the same number to both sides of an equation, which property of equality are you using?
Addition Property of Equality
5x = 20
How many solutions does this equation have?
One Solution and x = 4
Solve for y:
y + k = p
Subtract k on both sides
y = p − k
3(x − 4) + 2x = 28
x = 8
-3x + 5 ≤ -16
x ≥ 7
If 3x + 7 = 22, which property of equality would you use first to isolate x?
Subtraction Property of Equality
If solving an equation leads to a false statement like 10 = 31, how many solutions does it have?
No Solutions because 10 does not equal 31.
Solve for b:
ax + b = c
Subtract ax on both sides
b = c − ax
4x + 27 = -x + 42
x = 3
5x - 3 > 2x + 9
x > 4
True or False: The Multiplication Property of Equality states that you can multiply by different numbers on both sides of an equation and the equation will still be true.
False; you multiply by the same number on both sides of an equation.
True or False: If two sides of an equation are identical after simplifying, (like 8 = 8 or 5x - 2 = 5x - 2), the equation has one solution.
False — it has infinitely many solutions because we can choose any number for x and the equation will stay equal.
Solve for x:
m = pqx
Divide by pq on both sides
m/pq = x OR x = m/pq
7 − 2(3 − x) = x + 9
x = 8
x ≤ -5x
A teacher writes: 5x + 2 = 17. Explain step by step which properties of equality you would use to solve for x.
Step 1: Subtraction POE (subtract 2 on both sides)
Step 2: Division POE (divide 5 on both sides)
A student solves and ends up with x = 7 and says it only has one solution, why?
The equation only has one solution because it is only one value that makes the equation true, 7.
Solve for a:
p = 2a + 2b
1st subtract 2b on both sides
p − 2b = 2a
2nd divide by 2 on both sides
(p − 2b)/2 = a OR a = (p − 2b)/2
4x − 7 = 2(x + 5) + x
x = 17
3(x + 3) > 4(x − 4)
x < 25
A student writes:
Step 1: 5(x + 2) = 25
Step 2: 5x + 10 = 25.
Which property did they use, AND what would you do next?
Step 2: Distributive Property
Step 3: Subtraction POE
7x + 2 = 7x + 10
How many solutions does this equation have?
No solution. Because when we simplify the equation, we get 2 = 10 and 2 does not equal 10.
Solve for y:
Ax + By = C
1st subtract Ax on both sides
By = C − Ax
2nd divide by B on both sides
y = (C − Ax)/B