# +26 2.1 Practice A Algebra 1 Answers

## Introduction

Welcome to our blog article on 2.1 Practice A Algebra 1 answers. In this article, we will be exploring the various questions and answers from the 2.1 Practice A worksheet in Algebra 1. Whether you're a student looking to check your answers or a teacher seeking additional resources, this article will provide you with the solutions and explanations you need. So let's dive in and explore the world of Algebra 1!

### Question 1: Simplifying Expressions

In this question, you are asked to simplify the given expression: 3x + 2y - 4x + 5y.

To simplify this expression, we combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, the like terms are the x terms (3x and -4x) and the y terms (2y and 5y).

Combine the x terms: 3x - 4x = -x.

Combine the y terms: 2y + 5y = 7y.

Therefore, the simplified expression is: -x + 7y.

### Question 2: Solving Equations

In this question, you are asked to solve the equation: 2x - 5 = 9.

To solve this equation, we want to isolate the variable x. We can do this by performing inverse operations.

Add 5 to both sides of the equation: 2x - 5 + 5 = 9 + 5.

This simplifies to: 2x = 14.

Next, divide both sides of the equation by 2: (2x)/2 = 14/2.

This simplifies to: x = 7.

Therefore, the solution to the equation is x = 7.

### Question 3: Graphing Linear Equations

In this question, you are asked to graph the equation: y = 2x + 3.

To graph a linear equation, we need to plot at least two points and then connect them with a straight line. One way to find points on the graph is to create a table of values.

Let's choose some x values and substitute them into the equation to find the corresponding y values:

When x = 0, y = 2(0) + 3 = 3. So one point on the graph is (0, 3).

When x = 1, y = 2(1) + 3 = 5. So another point on the graph is (1, 5).

Plot these points on a coordinate plane and connect them with a straight line.

Therefore, the graph of the equation y = 2x + 3 is a line that passes through the points (0, 3) and (1, 5).

### Question 4: Factoring Quadratic Expressions

In this question, you are asked to factor the quadratic expression: x^2 + 6x + 8.

To factor a quadratic expression, we look for two binomials that multiply to give us the original expression.

In this case, we need to find two binomials in the form (x + ?)(x + ?) that multiply to give us x^2 + 6x + 8.

We can start by looking for factors of 8 that add up to 6. The factors of 8 are 1, 2, 4, and 8.

The pair of factors that add up to 6 is 2 and 4.

Therefore, the factored form of the quadratic expression x^2 + 6x + 8 is (x + 2)(x + 4).

### Question 5: Solving Systems of Equations

In this question, you are asked to solve the system of equations:

2x - y = 4

x + y = 6

There are multiple methods to solve systems of equations, such as substitution, elimination, or graphing. Let's use the elimination method in this case.

To eliminate one variable, we can add the two equations together:

(2x - y) + (x + y) = 4 + 6

This simplifies to: 3x = 10

Next, divide both sides of the equation by 3: (3x)/3 = 10/3

This simplifies to: x = 10/3

Now, substitute the value of x back into one of the original equations to solve for y:

x + y = 6

(10/3) + y = 6

Subtract (10/3) from both sides of the equation: y = 6 - (10/3)

This simplifies to: y = 8/3

Therefore, the solution to the system of equations is x = 10/3 and y = 8/3.

### Question 6: Simplifying Radicals

In this question, you are asked to simplify the given radical expression: √12.

To simplify a radical expression, we want to find the largest perfect square factor of the number inside the radical.

In this case, the largest perfect square factor of 12 is 4.

Therefore, we can rewrite √12 as √(4 * 3).

Next, we can split the radical into two separate radicals:

√(4 * 3) = √4 * √3

We know that √4 = 2, so the final simplified form of the radical expression √12 is 2√3.

### Question 7: Solving Inequalities

In this question, you are asked to solve the inequality: 3x + 5 > 10.

To solve this inequality, we want to isolate the variable x. We can do this by performing inverse operations, just like solving an equation.

Subtract 5 from both sides of the inequality: 3x + 5 - 5 > 10 - 5

This simplifies to: 3x > 5

Next, divide both sides of the inequality by 3: (3x)/3 > 5/3

This simplifies to: x > 5/3

Therefore, the solution to the inequality is x > 5/3.

### Question 8: Evaluating Functions

In this question, you are asked to evaluate the function f(x) = 2x^2 - 3x + 4 for a given value of x.

To evaluate a function, we substitute the given value of x into the function and simplify.

Let's say we need to evaluate the function f(x) = 2x^2 - 3x + 4 for x = 2.

Substitute x = 2 into the function: f(2) = 2(2)^2 - 3(2) + 4

This simplifies to: f(2) = 2(4) - 6 + 4

This further simplifies to: f(2) = 8 - 6 + 4

Therefore, f(2) = 6.

### Question 9: Solving Absolute Value Equations

In this question, you are asked to solve the absolute value equation: |2x - 3| = 7.

To solve an absolute value equation, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: 2x - 3 > 0

In this case, we can remove the absolute value symbols and solve the equation as usual:

2x - 3 = 7

Add 3 to both sides of the equation: 2x - 3 + 3 = 7 + 3

This simplifies to: 2x = 10

Next, divide both sides of the equation by 2: (2x)/2 = 10/2

This simplifies to: x = 5

Case 2: 2x - 3 < 0

In this case, we need to flip the inequality sign when we remove the absolute value symbols:

-(2x - 3) = 7

Distribute the negative sign: -2x + 3 = 7

Subtract 3 from both sides of the equation: -2x + 3 - 3 = 7 - 3