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Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 5 - Systems and MatricesProblem 48
Chapter 6, Problem 48

Solve each equation.
Matrix equation with variables and constants set equal to an expression, prompting to solve each equation.

Verified step by step guidance
1
First, identify the equation you need to solve. It seems the equation is incomplete as given, but typically, an equation involving 2x might look like \(2x = \text{some expression}\). Make sure you have the full equation before proceeding.
Assuming the equation is something like \(2x = a\), where \(a\) is a constant or an expression, the goal is to isolate \(x\) on one side of the equation.
To isolate \(x\), divide both sides of the equation by 2. This gives \(x = \frac{a}{2}\).
If the right side of the equation is more complex (for example, an expression involving \(x\) or other variables), first simplify that expression as much as possible before isolating \(x\).
After isolating \(x\), check your solution by substituting it back into the original equation to verify that both sides are equal.

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Key Concepts

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

Understanding Equations

An equation is a mathematical statement that asserts the equality of two expressions. Solving an equation involves finding the value(s) of the variable(s) that make the equation true. Recognizing the structure of the equation is essential to apply appropriate methods.
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Categorizing Linear Equations

Isolating the Variable

To solve for a variable, you need to isolate it on one side of the equation. This often involves performing inverse operations such as addition, subtraction, multiplication, or division to both sides, maintaining equality while simplifying the expression.
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Equations with Two Variables

Interpreting and Correcting Equation Format

The given equation appears incomplete or improperly formatted (e.g., missing left side expression). Understanding how to interpret or rewrite the equation correctly is crucial before solving, ensuring clarity on what is being equated to 2x.
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Solving Quadratic Equations by Factoring
Related Practice
Textbook Question

Let A=[−2403]A = \(\left\)[ \(\begin{matrix}\) -2 & 4 \\ 0 & 3 \(\end{matrix}\) \(\right\)] and B=[−6240]B = \(\left\)[ \(\begin{matrix}\) -6 & 2 \\ 4 & 0 \(\end{matrix}\) \(\right\)] . Find each of the following.

-A + (1/2)B

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

∣01−37521−26∣\(\begin{vmatrix}\)0&1& -3\\7& 5 &2\\ 1&-2&6\(\end{vmatrix}\)

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Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

∣−414201024∣\(\begin{vmatrix}\) -4 & 1 & 4\\ 2& 0 & 1\\ 0&2&4 \(\end{vmatrix}\)

Textbook Question

Use the determinant theorems to evaluate each determinant.

∣68−12−10240−8∣\(\left\)| \(\begin{matrix}\) 6 & 8 & -12 \\ -1 & 0 & 2 \\ 4 & 0 & -8 \(\end{matrix}\) \(\right\)|

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Textbook Question

Graph the solution set of each system of inequalities.

y ≥ (x - 2)2 + 3

y ≤ -(x - 1)2 + 6

Textbook Question

Graph the solution set of each system of inequalities.

y ≥ x2 + 4x + 4

y < -x2