Evaluating and Expressions
A number is decreased by 45. The result is then divided by 12. Then 20 is added to the new result. This gives a final result of 30.
165
n + 39 = 12
n = -27
6 - 2y = 9y + 13
x = -1
|x + 2| = 4
x = 2 , -6
Three fifth of what number equals one?
3/5 x = 1
x = 1/5
Translate into a verbal sentence
2x + 3y = y2 – 2
The sum of double x and triple y, is the same as 2 less than y squared
w + (-8) = -21
w = -13
5(7 – a) – 3(a + 4) – 4 = 4(a –3) + 7
35 - 5a - 3a -12 -4 = 4a -12 + 7
-2a = -28
a = 14
|4m + 6| = 2
m = -1 , -2
The product of 2 more than a number and 10 is 36 more than 8 times the number. What is the number?
10(x + 2) = 8x + 36
x = 8
Write an algebraic expression for
Twice the difference of a number and 7
2(x - 7)
-6n = 16
n = -16/6 = -8/3
Solve ax - n = r for x
(r + n) / a = x
|2t + 5| -7 = 2
t = 2 , -7
State whether the percent of change is a percent of increase or a percent of decrease. Then find the percent of change.
original: 75, new: 84
9/75 = x/100
12% Increase
Evaluate:
2|m - 3x| - p if m = -1, x = 2 and p = 4
-18
3/4h = -45/52
h = -15/13
x/2 + 1/3 = 4/3
x = 2
|x - 6| = -5
impossible
Two airplanes leave the Atlanta airport at the same time, traveling in opposite directions. One plane travels 30 miles per hour faster than the other. After 3 hours, the planes are 3150 miles apart. What is the rate of each plane?
3(x) + 3(x+30) = 3150
6x + 90 = 3150
6x = 3060
x = 510 other plane 540
The length of a rectangle is x + 9
The width is 5
Write an expression for the perimeter. AND another for the area
Perimeter: 5 + 5 + x + 9 + x + 9 = 2x + 28
Area: 5(x+9)
-a/6 + 7 = -14
a = 126
Solve the proportion
t+4 = 1
t - 2 4
4t + 16 = t - 2
t = -6
Dennis is buying a snowboard, the average price is $600 by the price can vary by up to $230. Write and solve an equation to find the upper and lower bounds of Snowboard prices.
|x - 600| = 230
x = 370, 830
How much of a %30 acid solution should be added to 5 liters of 60% acid solution in order to have a 50% acid solution?
0.3x + 0.6(5) = 0.5(x + 5)
0.3x + 3 = 0.5x + 2.5
0.5 = 0.2x
x = 2.5 liters