Solve each linear equation. See Examples 1–3. 7x + 8 = 1

Verified step by step guidance

Identify the given linear equation: \(7x + 8 = 1\).

Isolate the term containing \(x\) by subtracting 8 from both sides: \(7x + 8 - 8 = 1 - 8\) which simplifies to \(7x = 1 - 8\).

Simplify the right side of the equation: \(7x = -7\).

Solve for \(x\) by dividing both sides by 7: \(x = \frac{-7}{7}\).

Simplify the fraction to find the value of \(x\).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. It represents a straight line when graphed. Solving a linear equation involves finding the value of the variable that makes the equation true.

Isolating the Variable

Isolating the variable means manipulating the equation to get the variable alone on one side. This typically involves performing inverse operations such as addition, subtraction, multiplication, or division to both sides of the equation to maintain equality.

Properties of Equality

Properties of equality state that you can add, subtract, multiply, or divide both sides of an equation by the same nonzero number without changing the equation's solution. These properties are essential for maintaining balance while solving equations.

Recommended video:

2:20

Imaginary Roots with the Square Root Property

Related Practice

Textbook Question

For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the midpoint M of line segment PQ. See Examples 1 and 2. P(-5, -6), Q(7, -1)

520

views

Textbook Question

Find each sum or difference. See Example 1. -6 + (-13)

500

views

Textbook Question

Find the domain of each rational expression. See Example 1. (x + 3) / (x - 6)

963

views

Textbook Question

Find each square root. See Example 1. √100