Algebra Definitions and Equations

Questions and Answers

What is the definition of variable?

An unknown amount, represented by a letter

What is the definition of coefficient?

A number that is multiplied by the variable

What is the definition of constant?

A number that stands alone (without a variable) in an expression

What is the definition of term?

A combination of constants and variables, separated by operators/operations Signup and view all the answers

What is the definition of algebraic expression?

A collection of numbers, variables, and operators (with no equals sign), packaged into a mathematical phrase Signup and view all the answers

What is the definition of numerical expression?

An expression with no variables in it (numbers and operators only) Signup and view all the answers

What is the definition of inverse operation?

When you do the opposite operation than the operation in the equation Signup and view all the answers

What are the 6 steps to solve a shadow problem?

First, make the 'L's. Next, plug in what you know. Then, set up a proportion. After, cross multiply and it's a 2 step problem to solve for x. Finally, plug in x and make sure it is correct. Signup and view all the answers

Solve for x: 3x = -21.6

x = -7.2 Signup and view all the answers

Solve for x: -x/8 = 12

x = -96 Signup and view all the answers

Solve for x: 11.6 + 3x = -16.9

x = -9.5 Signup and view all the answers

Solve for x: x/9 - 7 = 3

x = 20 Signup and view all the answers

Solve for b: 2/3(9b - 7) = 36

b = 9 Signup and view all the answers

Solve for x: 0.5(2x - 4) = -17

x = -15 Signup and view all the answers

Solve for p: 14p - 8 = 22 + 20p

p = -5 Signup and view all the answers

Use the distributive property to write each expression as an equivalent equation: 13(10 - 7)

39 Signup and view all the answers

Solve for x: (1.15 + 0.8x) = (2.3 - 1.5x)

x = 0.5 Signup and view all the answers

Solve for x: x/4 + 9 = 3x - (18 + 6)

x = 12 Signup and view all the answers

Supplementary angles are 2 angles in which the sum of their angle measures is ______ degrees.

180 Signup and view all the answers

Complementary angles are 2 angles in which the sum of their angle measures is ______ degrees.

90 Signup and view all the answers

Angles 1 and 2 are complementary angles. Angle 1 is 37 degrees, so what is the angle measure of angle 2?

Angle 2 = 53 degrees Signup and view all the answers

Angles 1 and 2 are supplementary angles. Angle 1 is 45 degrees, so what is the angle measure of angle 2?

Angle 2 = 135 degrees Signup and view all the answers

How do you check to prove that your answer to an algebra problem is correct?

You can plug the answer into the equation to replace the unknown variable. Do the equation with the number plugged in to be sure that your answer is correct. Signup and view all the answers

The sum of 3 consecutive integers is 72. Write and solve an equation to find the integers.

(x + 1) + x + (x - 1) = 72; (24 - 1) + 24 + (24 + 1) = 72 Signup and view all the answers

The sum of 4 consecutive odd integers is 216. Write and solve an equation to find the integers.

(x - 2) + x + (x + 2) + (x + 4) = 216; (53 - 2) + 53 + (53 + 2) + (53 + 4) = 216 Signup and view all the answers

Study Notes

Definitions in Algebra

Variable: An unknown amount shown by a letter in mathematical expressions.
Coefficient: A numerical factor that multiplies the variable in an algebraic term.
Constant: A standalone number without a variable in an expression.
Term: A combination of constants and variables, typically linked with addition or subtraction.
Algebraic Expression: Contains numbers, variables, and operators, but does not include an equals sign.
Numerical Expression: Composed only of numbers and operators without any variables present.
Inverse Operation: The process of applying the opposite mathematical operation to solve an equation.

Steps and Methods

Steps to Solve a Shadow Problem:
- Create "L" shapes for clarity.
- Input known values.
- Establish a proportion.
- Cross-multiply, followed by a two-step solution for x.
- Substitute x back into the original equation to verify accuracy.

Solving Equations

Equation Solutions:
- 3x = -21.6 results in x = -7.2
- -x/8 = 12 leads to x = -96
- 11.6 + 3x = -16.9 gives x = -9.5
- x/9 - 7 = 3 yields x = 20
- 2/3(9b - 7) resolves to b = 9
- 0.5(2x - 4) = -17 results in x = -15
- 14p - 8 = 22 + 20p gives p = -5
- (1.15 + 0.8x) = (2.3 - 1.5x) leads to x = 0.5
- x/4 + 9 = 3x - (18 + 6) solves for x = 12

Angles

Supplementary Angles: Two angles that add up to 180 degrees.
Complementary Angles: Two angles that sum to 90 degrees.
Calculating Angles:
- If angle 1 is 37 degrees (complementary), angle 2 equals 53 degrees.
- If angle 1 measures 45 degrees (supplementary), angle 2 is 135 degrees.

Verification

Checking Answers: Substitute the found value back into the original equation to confirm the solution is correct through computation.

Consecutive Integers Problems

Three Consecutive Integers: Their combined sum is represented by the equation ((x+1) + x + (x-1) = 72).
Four Consecutive Odd Integers: Formulated as ((x-2) + x + (x+2) + (x+4) = 216).

These highlights encapsulate essential algebraic concepts, problem-solving techniques, and angle relationships vital for understanding the topic.

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Test your knowledge of key algebra concepts including variables, coefficients, and algebraic expressions. This quiz also explores methods for solving equations and shadow problems. Perfect for reinforcing fundamental algebra techniques.