In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 10x + 3 = 8x + 3

Verified step by step guidance

Start by writing down the given equation: $10x + 3 = 8x + 3$.

To isolate the variable terms on one side, subtract \$8x$ from both sides: $10x + 3 - 8x = 8x + 3 - 8x$, which simplifies to $2x + 3 = 3$.

Next, subtract 3 from both sides to isolate the term with $x$: $2x + 3 - 3 = 3 - 3$, which simplifies to $2x = 0$.

Now, solve for $x$ by dividing both sides by 2: $\frac{2x}{2} = \frac{0}{2}$, which simplifies to $x = 0$.

Finally, analyze the solution: since you found a specific value for $x$, the equation is a conditional equation (true only for $x = 0$).

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.

Solving Linear Equations

Solving linear equations involves isolating the variable on one side of the equation using inverse operations such as addition, subtraction, multiplication, or division. The goal is to find the value of the variable that makes the equation true.

Types of Equations: Identity, Conditional, and Inconsistent

An identity is true for all values of the variable, a conditional equation is true for specific values, and an inconsistent equation has no solution. Identifying the type depends on the solution set after solving the equation.

Properties of Equality

Properties of equality, such as the addition, subtraction, multiplication, and division properties, allow manipulation of equations without changing their solutions. These properties are essential for maintaining balance while solving equations.

Recommended video:

5:36

Change of Base Property

Related Practice

Textbook Question

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 5x + 7 = 2x + 7

675

views

Textbook Question

In Exercises 59–94, solve each absolute value inequality. |(2x + 2)/4| ≥ 2

582

views

Textbook Question

Exercises 73–75 will help you prepare for the material covered in the next section. Rationalize the denominator: (7 + 4√2)/(2 - 5√2).

1005

views

Textbook Question

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| + 3 = 3