Writing Equations
Write an algebraic equation.
The product of three and a number increased by ten is the same as fourteen.
3x + 10 = 14
Solve for the variable:
26 = 8 + v
v=18
Solve the inequality:
7x<=42
x<=6
Graph on a number line:
x<5
Write an algebraic equation.
The product of four and the sum of x and y is the same as seven subtracted from z.
4(x + y) = z - 7
Solve for the variable
x/4=6
x=24
Solve the inequality:
2x-5>15
x>10
Graph on a number line:
x>=-5
Write an algebraic equation.
The sum of four and b multiplied by the sum of x and y is equivalent to the product of seven and z.
(4 + b)(x + y) = 7z
Solve:
-3(y+5) = 18
y = -11
Solve the inequality:
-6x+7<13
x> -1
Graph on a number line:
x<–2 or x>5
Translate the statement into an equation.
3 times the sum of a number and 4 is the same as 5 times the quantity of the same number subtracted from 11.
3(x + 4) = 5(11 - x)
Solve:
2(x – 1) = 2x + 5
no solutions
Solve the inequality:
4n + 1 > 9 or n + 3 < 1
n > 2 or n < –2
Graph on a number line:
x>=1 and x<7
Translate the statement into an equation.
One half the difference of a number and 2 is equivalent to 3 times the quantity of the same number added to 7.
1/2(n-2)=3(n+7)
Solve:
5/x=2/8
x=20
Solve the inequality:
-8<2x+4<=12
-6<x<4
Graph on a number line:
-5<x<2