Algebra Chapter 1: Expressions and Equations

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Questions and Answers

What is the result of $-2[3 - (-2)(6)]$?

-36

-18

-24

-30 (correct)

What is the first operation to perform in the expression $(-4)^2 + 2[12 + (3 - 5)]$?

-4 (correct)

In the expression $(5a^2 - 3a + 1) - (2a^2 - 4a + 6)$, what must you do before combining like terms?

-6

-1 (correct)

When solving equations, which operation should be tackled first?

3 Signup and view all the answers

If you have the equation $x + 5 = 15$, what is the first step to isolate $x$?

<ul> <li>5</li> </ul> Signup and view all the answers

In the expression $2x + 4[2 - (5x - 3)]$, what should you perform first?

5 Signup and view all the answers

Which of the following statements about solving equations is true?

You must maintain equality by doing the same operation on both sides. Signup and view all the answers

What is the result of simplifying the expression $x^2 + 5x + 3x^2 + x^3 - 5 + 3$?

$x^3 + 4x^2 + 5x - 2$ Signup and view all the answers

Which of the following statements correctly distinguishes between an expression and an equation?

An expression does not have an equal sign, while an equation does. Signup and view all the answers

Which operation should be performed first when simplifying the expression $3 + 4 × (2 - 1)$ according to PEMDAS?

Parentheses Signup and view all the answers

What is the main objective when simplifying an expression?

Combine like terms to reduce the number of terms. Signup and view all the answers

In the expression $10x - 5x + 4 - 6$, what is the simplified form of the constant terms?

2 Signup and view all the answers

What is the first step to take when simplifying the expression $(x - 3)(x + 2)$?

Use the distributive property to expand. Signup and view all the answers

Which operation is performed after simplifying any parentheses when following the order of operations?

Exponentiation Signup and view all the answers

If you have the expression $x^2 + 3x - 9 + 5 - 2x$, what is the coefficient of $x$ after simplification?

1 Signup and view all the answers

What is the equation to find the perimeter of the yard given the width and length?

p = 2l + 2w Signup and view all the answers

If the width of the yard is represented by w, what expression correctly represents the length?

l = 2w + 3 Signup and view all the answers

How would you simplify the equation 48 = 2(2w + 3) + 2w using the distributive property?

48 = 4w + 6 + 2w Signup and view all the answers

After combining like terms, what is the equation obtained from 48 = 4w + 6 + 2w?

48 = 6w + 6 Signup and view all the answers

What is the width of the yard once solved from the equation 42 = 6w?

7 ft Signup and view all the answers

What is the length of the box if the width is calculated to be 6 in, given the volume formula V = lwh?

12 in Signup and view all the answers

What is the first step in solving the equation $x + 9 = -6$?

Subtract 9 from both sides. Signup and view all the answers

If a box has a volume of 360 in³, a length of 12 in, and a height of 5 in, what equation must be solved for width?

360 = 12 * 5 * w Signup and view all the answers

In the inequality x < 10, which part of the sign indicates that x is less than 10?

The small side of the sign Signup and view all the answers

When solving the equation $5x - 7 = 2$, what operation should you perform first?

Add 7 to both sides. Signup and view all the answers

In the equation $7(x + 4) = 6x + 24$, what is the first step to simplify the left-hand side?

Distribute the 7. Signup and view all the answers

What should you do to both sides of the equation $7x + 28 = 6x + 24$ to isolate the variable term?

Subtract 6x from both sides. Signup and view all the answers

What is the result of the equation $2(x - 1) = -3$ when solved for x?

x = -1/2 Signup and view all the answers

Why are word problems considered challenging in mathematics?

They need translation from words to equations. Signup and view all the answers

What is the second important step in translating a word problem into an equation?

Identify the variables. Signup and view all the answers

In problem-solving, what is the primary focus to develop logical reasoning?

Accepting the challenge of word problems. Signup and view all the answers

What is the total length of the fence around the rectangular yard?

48 feet Signup and view all the answers

If the width of the yard is represented by $w$, how can the length $l$ be expressed in terms of $w$?

$l = 2w + 3$ Signup and view all the answers

Which formula correctly represents the perimeter of the yard?

$p = 2l + 2w$ Signup and view all the answers

How would you rearrange the equation $2w + 3 = l$ to express $w$ in terms of $l$?

$w = \frac{l - 3}{2}$ Signup and view all the answers

If the width of the yard is 10 feet, what would be the length of the yard?

23 feet Signup and view all the answers

What is the first step in solving for the dimensions of the yard?

Understand and define the variables. Signup and view all the answers

Which of the following statements is NOT true based on the information provided?

The length is always less than the width. Signup and view all the answers

What must be known to find the yard's length directly?

The width of the yard. Signup and view all the answers

Study Notes

Simplifying Expressions

An expression is a mathematical phrase that contains numbers and variables, but no equal sign.
Like terms have the same variables and exponents and can be combined by adding or subtracting their coefficients.
PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) is the order of operations to simplify expressions.

Solving Equations

An equation has an equal sign.
The goal is to isolate the variable (solve for x).
To solve for x, use reverse order of operations (PEMDAS) and perform the same operations on both sides of the equation.
To move variables from one side of the equation to the other, add or subtract them as needed.

Problem Solving

Word problems provide real-world applications of algebra.
Three steps to solve word problems:
- Understand the problem: Analyze the given information and identify what needs to be found.
- Define variables: Assign letters to the unknown quantities.
- Write an equation: Translate the words into a mathematical equation using the defined variables.

Inequalities

An inequality uses symbols (<, >, ≤, ≥) to express relationships between values.
The "<" symbol indicates "less than", the ">" symbol indicates "greater than", and the "≤" and "≥" symbols include equality.
Solving inequalities follows similar rules as solving equations, with the exception that multiplying or dividing by a negative number flips the inequality sign.

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Description

This quiz covers the basics of simplifying expressions and solving equations in algebra. Learn how to identify like terms, apply the order of operations, and tackle real-world word problems. Test your understanding of key concepts and strategies to isolate variables and solve for x.