Algebra I Review: Equations, Proportions, and Word Problems

Flashcards testing linear equations, absolute value equations, proportions, number of solutions, and word problems from the lecture notes.

Solve for $b$: $-\frac{7}{8} = -\frac{1}{3}b + \frac{3}{4}$

$$b = \frac{39}{8}$$

Solve for $a$: $-\frac{1}{2} + \frac{1}{3}a = \frac{1}{8}$

$$a = \frac{15}{8}$$

Solve for $x$: $-12x - 2 = -7x - 17$

$$x = 3$$

Solve for $x$: $3x + 1 = -2x + 36$

$$x = 7$$

Solve for $x$: $7x - 3(9x + 4) = 9(-x - 1) + x$

$$x = -\frac{1}{4}$$

Solve for $x$: $6(4x + 5) = 3x - 4(-4x - 1) + 5$

$$x = -\frac{21}{5}$$

Solve for $x$: $4 = \frac{3}{8}(6x + 16)$

$$x = -\frac{8}{9}$$

Which value of $x$ satisfies the equation $\frac{2}{3}\big(x + \frac{1}{2}\big) = -3$?

$$x = -5$$

How many solutions exist for the equation $x + 1 = 1 + x$?

Infinite solutions (Identity)

How many solutions exist for the equation $x = x - 5$?

No solutions (Contradiction)

How many solutions exist for the equation $-4x = 28$?

One solution ($x = -7$)

Solve for all values of $a$: $18 = |6a|$

$a = 3$ and $a = -3$

Solve for all values of $x$: $17 = |x - 13|$

$x = 30$ and $x = -4$

Solve for all values of $a$: $17 = |2 - 5a|$

$a = -3$ and $a = \frac{19}{5}$

Solve for all values of $y$: $|5y - 3| = 28$

$y = \frac{31}{5}$ and $y = -5$

Solve for $x$: $\frac{3}{4} = \frac{21}{x}$

$$x = 28$$

Solve for $x$: $\frac{x}{20} = -\frac{2}{5}$

$$x = -8$$

Solve for $x$: $\frac{x - 9}{3} = \frac{x - 3}{2}$

$$x = -9$$

Solve for $x$: $\frac{6}{2x - 2} = \frac{5}{2x - 9}$

$$x = 22$$

Solve for $x$: $4(5x - 7) = -4(-5x + 7)$

infinite solutions

Solve for $x$: $5(-2x - 3) = 9x + 21$

$$x = -\frac{36}{19}$$

Lamonte took his computer to a repair store. The technician worked on it for $4.25\text{ hours}$ and charged him $\text{\\textdollar}141$ for parts. The total was $\text{\\textdollar}544.75$. What was the cost of labor, per hour?

$\text{\\textdollar}95$ per hour

Members of a soccer team raised $\text{\\textdollar}1816.50$ to go to a tournament. They rented a bus for $\text{\\textdollar}880.50$ and budgeted $\text{\\textdollar}58.50$ per player for meals. Determine the number of players the team can bring to the tournament.

$$16\text{ players}$$

Maya buys $15\text{ bottles}$ of grapefruit juice for a total cost of $\text{\\textdollar}16.65$. If each bottle costs the same amount, how much do $14\text{ bottles}$ of juice cost?

$$\text{\\textdollar}15.54$$

A $6\frac{1}{4}\text{-inch}$ candle burns down in $5\text{ hours}$. Assuming the candles are directly proportional, how long would it take a $5\text{-inch}$ candle to burn down?

$$4\text{ hours}$$

The number of miles driven by Khloe is directly proportional to the number of gallons she used. How many miles would she drive on $26\text{ gallons}$?

$$938.6\text{ miles}$$