Writing Equations
Translate into algebraic equation:
The difference of f and 5 is twenty-two.
f - 5 = 22
Solve c - 22 = 54
c = 76
Solve 11x - 4 = 29
x = 3
Solve 2 + 5k = 3k - 6
k = -4
Evaluate |m + 6| - 14 if m = 4
= -4
Translate into algebraic equation:
Four times the sum of 14 and c is a squared.
4(14 + c) = a2
Solve j - 87 = -3
j = 84
Solve (n+1)/(-2)= 15
n = -31
Solve 6(5m - 3) = 1/3(24m + 12)
m = 1
Evaluate expression if a = -2, b = -3, c = 2
4a - |3b + 2c|
= -13
Translate into algebraic equation and solve:
Thirteen times a number t minus twelve equals forty.
Equation: 13t − 12 = 40
Answer: t = 4
Solve -1/4 = 2/3b
b = -3/8
Find three consecutive odd integers with a sum of 75. Write an equation and solve.
Equation: n + (n + 2) + (n + 4) = 75
Answer: 23, 25, 27
Solve 5x + 5 = 3(5x - 4) - 10x
5 ≠ -12 (NO SOLUTION)
Solve equation.
|-4d + 6| = 12
{-3/2, 9/2}
Translate into algebraic equation and solve:
A number m minus 8 is the same as a number m divided by 2.
Equation: m - 8 = m/2 or m - 8 = 1/2(m)
Answer: m = 16
Solve -2/3h = -22
h = 33
Find four consecutive integers with the sum of -142. Write an equation and solve.
Equation: n + (n + 1) + (n + 2) + (n + 3) = -142
Answer: -37, -36, -35, -34
Find the value of x so that the figures have the same perimeter.
rectangle #1 (length = 6, width = x) rectangle #2 (length = 2x + 2, width = x)
x = 2
Solve equation and graph.
4 - 3|q| = 10
no solution (blank graph)
Lou wants to lose weight to audition for a part in a play. He weighs 160 pounds now. He wants to weigh 150 pounds.
1. Write an equation to represent this situation.
2. How many pounds does he need to lose to reach his goal?
1. 160 - x = 150
2. x = 10 lbs
An electronics store sells a certain digital camera for $126. This is 2/3 of the price that a photography store charges. What is the cost of the camera at the photography store? Write equation and solve.
Equation: 126 = 2/3c
Answer: $189
Solve for x. Assume a ≠ 0.
ax + 7 = 5
x = -2/a
Find the value of x so that the figures have the same perimeter.
triangle (side one = 3x + 4, side two = 5x + 1, side three = 2x + 5)
rectangle (length = x + 13, width = 2x)
x = 4
Write an equation involving absolute value.
Closed dot on -3 and 5
|x - 1| = 4