Writing equations
Translate to an algebraic equation:
"Five more than twice a number n is 17."
2n + 5 = 17
Solve for x:
x - 14 = -6
x = 8
Solve for x:
3x + 8 = 29
x=7
Solve for m:
2(m + 4) = 18
M= 5
Solve for x and state rule:
-4x < 20
Answer: x > -5 (Flip inequality when dividing by
negative)
Translate to an equation:
"The product of 4 and a number x, decreased by 9, equals 15."
4x - 9 = 15
Solve for y:
-7y = 56
Answer: y = -8
Solve for a:
(a / 4) - 5 = 3
Answer: a = 32
Solve for x:
5(x - 2) = 3x + 6
x= 8
Solve two-step inequality:
2x - 5 ≥ 7
Answer: x ≥ 6
Translate to an equation:
"Seven less than the quotient of a number y and 3 is
11."
Answer: (y / 3) - 7 = 11
Solve for a:
a / -5 = -9
Answer: a = 45
Solve for p:
-6p + 15 = -21
p=6
Solve for k:
4(k - 3) + 2k = 24
k = 6
Solve inequality:
-3n + 8 > -7
Answer: n < 5
Translate to an equation:
"Three times the sum of a number k and 4 is 27."
Answer: 3(k + 4) = 27
Solve for m:
m + 18.5 = 7.2
Answer: m = -11.3
Solve for n:
14 - 2n = 38
Answer: n = -12
Solve for b:
-3(2b - 5) = 33
Answer: b = -3
Solve compound inequality:
-2 ≤ x + 3 < 8
Answer: -5 ≤ x < 5
Translate to an equation:
"The difference of twice a number x and 8 is equal to 5 times the same number x plus 4."
Answer: 2x - 8 = 5x + 4
Solve for fraction coefficient:
(-3/4)w = 18
Answer: w = -24
Solve for y:
(2/3)y - 7 = 13
Answer: y = 30
Solve for z:
2(3z - 4) - 5(z + 1) = 9
z= 22
Solve multi-step inequality:
5 - 2(x - 3) ≤ 17
Answer: x ≥ -3