Literal Equations
2x + 3y = 12. Solve for x
x = 6 - 3/2y
4x - 3 = 2x + 5
x = 4
2y + 3x + 7y - x
9y + 2x
-3r < 10 - r
r > -5
Identify the number of solutions to 2x + 10 = 2(x + 5).
Infinite Solutions
5j + s = t - 2. Solve for t
t = 5j + s + 2
2(2t - 3) = 6(t + 2)
t = -9
3x + 7 - 5x + (-9)
-2x - 2
2(6 - x) < 4x
x > 2
Identify the number of solutions to 2x + 5 = 2(x + 3).
No solution
Solve x/r = v for x.
x = rv
7(14 - x) = -3(-x - 6)
x = 8
9y + 4x - 7 - 3 + (-x) + y
10y + 3x - 10
4(y + 1) < 4y + 2
no solution
3(2x - 5) = 2(3x - 2)
no solution
Solve h + p = 3(k - 8) for k.
k = h/3 + p/3 + 8
On the first day of the year, Diego had $700 in his savings account and started spending $35 a week. His brother Juan had $450 and started saving $15 a week. After how many weeks will the brothers have the same amount?
5 weeks
5 - 3x - 2(3 - x)
-1 - x
12(1/3x -1/4) > 9 - 2x
x > 2
Identify the number of solutions to 3x + 21 = 3(x + 7)
Infinite solutions
Solve m/n = p - 6 for n.
n = m/(p-6)
Write and solve an equation to answer the question below.
Lela purchased 3 mechanical pencils and a notebook that cost $5. Her purchase totaled $11. How much was each pencil? Use p to represent the cost of each pencil.
3p + 5 = 11; Each pencil costs $2
12(x - 5) - 30 + (-10) + x(3 + 6) + 1
21x - 99
Amarilys wants to buy tomatoes and a loaf of bread. Tomatoes are $1.20 a pound, and a loaf of bread is $2.00. She has $8.00 to spend but wants to have some change leftover.
How many pounds of tomatoes can she buy without spending all of her money?
Write the inequality and solve the problem. Let x be the number of pounds of tomatoes.
The cost of the tomatoes ($1.20x) plus the cost of the bread ($2.00) must be less than or equal to $8.00.
1.20x + 2.00 < 8.00
x < 5
She can buy up to 4 pounds of tomatoes.
Is 5 a solution to the inequality? 4x > 3(7 - x)
x > 3; yes