Simple Equations
Solve: 𝑛+3=−7
n=-10
Solve: 0.05w = 1.4
w=25
Solve: -2x = 3x + 10
x=-2
Solve: |x - 4| = 10
x = 14 or x = -6
Rewrite: 3y - x = 9, solve for y
y = (x+9)/3
Solve: 𝑧÷25=−4.5
𝑧=-112.5
Solve: 17 = 7 + 4(2.2d - 8.5)
d=5
Solve: 0.5(6h - 4) = -5h + 1
h=0.5
Solve: |2x + 3| = 9
x = 3 or x = -6
Rewrite: 2x + kx = m, solve for x
x = m/(2+k)
What does it mean for two equations to be equivalent?
They have the same solution set.
Define solution in the context of an equation
A value that makes the equation true
What does it mean if an equation has infinitely many solutions?
Both sides simplify to the same expression (true for all values).
What are the two equations when solving |x| = a?
x = a or x = -a
Solve cone surface area S = πr² + πrℓ for ℓ
ℓ = (S - πr²)/(πr)
Solve: -2n + 3 = 9
n=-3
Solve: 5(3 - x) + 2(3 - x) = 14
x=1
Solve: 3(2a - 2) = 2(3a - 3)
No Solution
Drone hovers 120 ft ± 8 ft. Write an equation.
|h - 120| = 8
Rewrite C = 5/9(F - 32) to solve for F
F = 9/5C + 32
Explain why the Addition Property of Equality is valid. Give an example.
Adding the same number to both sides keeps equality true. Example: x+2=5 → x=3
46 hrs worked, $462.56 earned, overtime 1.2x rate after 40 hrs. Find rate.
9.28
Boat problem: Upstream 4 hrs, downstream 2.8 hrs, 3 mph faster downstream. Find distance.
Distance = 33.6 miles
Plane flies 160 ± 25 miles at 150 mph. Solve for time.
t = (160 ± 25)/150 → 0.9 hrs ≤ t ≤ 1.23 hrs
Simple interest: $162.50 in 6 months on $5000. Solve for r.
r = 0.065 = 6.5%