Solving Simple Equations
Solve the equation. Justify the steps. Check your solution.
z + 3 = -6
z = -9; subtract 3 from each side
Solve the equation.
3y + 11 = -16
y = -9
Solve the equation.
3n - 3 = 4n + 1
n = -4
Solve the equation.
|y + 3| = 17
y = 14, y = -20
Solve the literal equation for y.
2x - 4y = 20
y = 1/2x - 5
Solve the equation. Justify the steps. Check your solution.
-n/5 = -2
n = 10; multiply each side by -5
Solve the equation.
6 = 1 - b
b = -5
Solve the equation.
2y - 16 = 1/3(y-3)
y = 9
Solve the equation.
2|k - 3| = 18
k = 12, k = -6
Solve the literal equation for y.
8x - 3 = 5 + 4y
y = 2x - 2
Solve the equation. Justify the steps. Check your solution.
πb = -1/9
b = -1/9π; divide each side by π
Solve the equation.
-4(2z + 6) - 12 = 4
z = -5
Solve the equation.
5(1 + x) = 5x + 5
all real numbers; infinite
Solve the equation.
|16g - 40| = -4|4g - 10|
g = 5/2
Solve the literal equation for y.
3(2x + y) = -4x - y
y = -5/2x
A cell phone costs $249.99. You have $175.29 in a savings account. You deposit an additional $48.75. How much more do you need to save to buy the cell phone?
$25.95
Solve the equation.
3/2(x - 2) - 5 = 15
x = 18
Solve the equation.
3(n + 4) = 1/2(6n + 4)
no solution
Solve the equation.
-2|5w -7| +9 = -7
w = 3, w = -1/5
Solve the literal equation for y.
a = 9y + 3yx
y = a/(9 + 3x)
Which property of equality should you use to solve the equation a/b + x = c, where a and b are negative numbers? Explain your reasoning.
Subtraction Property of Equality; because a and b are negative numbers, a/b is positive and the inverse operation is subtraction.
Find three consecutive odd integers that have a sum of 75.
23, 25, 27
An airplane leaves Los Angeles and travels 5 hours to New York City. The return trip travels along the same route and takes 6 hours and 15 minutes because the plane travels 99 miles per hour slower due to a headwind. Find the distance that the plane flies between the two cities.
2475 miles
Solve the equation.
-|b + 6| = |3b - 2|
no solution
The formula F = 9/5(K - 273.15) + 32 converts a temperature from kelvin K to degrees Fahrenheit F.
A. Solve the formula for K.
B. Convert 180 F to kelvin. Round your answer to the nearest hundreth.
A. K = 5/9(F - 32) + 273.15
B. 355.37 K