Algebra 1 Unit 3 Flashcards

What is the solution to the equation $x - 5 = -13$?

What is the solution to the equation $-8 = n - (-4)$?

Are the equations $17x = 85$ and $x = 5$ equivalent?

Are the equations $-16x = 48$ and $x = 3$ equivalent?

What is the solution to the equation $\frac{b}{2} = 14$?

What is the solution to the equation $14x + 3x - 40 = 11$?

Write and solve an equation to find the three consecutive integers that sum to 417.

What is the solution to the equation $3x - 8 = -3x + 4$?

If a gym charges $10 per hour as a non-member and $300 plus $4 per hour as a member, how many hours must you play as a non-member to justify becoming a member?

How wide can each picture be if you are designing a web page with 4 pictures, a width of 640, margins of 24, and 16 in between each picture?

What is the solution to the equation $-15x + 73 = 26$?

What is the solution to the equation $1.5x + 7.4 = -1.8x - 6.9$?

How can you rewrite the equation $6.2x + 4.5 = 3.8x + 7.9$ by multiplying by 10?

How do you solve for $b_1$ in the equation $A = \frac{1}{2}h(b_1 + b_2)$?

Rewrite the equation $3x + 5y = 15$ so that y is a function of x.

What is the unit rate for 3 tablespoons for 1.5 servings?

How many tablespoons are in 15 teaspoons, knowing that 1 tablespoon equals 3 teaspoons?

What percentage of people were in favor if 159 out of 350 were?

Solving Equations

For the equation x - 5 = -13, the solution is x = -8.
Solving the expression -8 = n - (-4) results in n = -12.
The equations 17x = 85 and x = 5 are equivalent, confirming the solution is consistent.
In contrast, -16x = 48 and x = 3 are not equivalent.

Algebraic Solutions

Solving b/2 = 14 gives b = 28.
The equation 14x + 3x - 40 = 11 simplifies to x = 3.

Consecutive Integers Problem

The sum of three consecutive integers can be expressed as x + (x + 1) + (x + 2) = 417, leading to x = 138.

Additional Equations

The equation 3x - 8 = -3x + 4 simplifies to find x = 2.
A financial problem described by 10h = 300 + 4h results in h = 50 hours for nonmembers to consider membership.

Geometry and Design

For a webpage with 4 pictures within a width of 640, accounting for margins and spacing leads to each picture being 136 in width.
The equation -15x + 73 = 26 resolves to x = 3.13.

More Algebraic Manipulations

The equation 1.5x + 7.4 = -1.8x - 6.9 simplifies to x = -4.33.
An equivalent equation of 6.2x + 4.5 = 3.8x + 7.9 after multiplying by 10 is 62x + 45 = 38x + 79.

Geometry Formula

Solving for b1 in the formula A = 1/2h(b1 + b2) results in the expression b1 = (2A/h) - b2.

Functions

The equation 3x + 5y = 15 can be rewritten to express y as a function of x: y = 3 - (3/5)x.

Unit Rate and Conversion

The unit rate for 3 tablespoons serving 1.5 servings is calculated to be 2.
Converting 15 teaspoons into tablespoons results in 5 (1 tablespoon = 3 teaspoons).