Ch. 1 - Equations and Inequalities

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 1 - Equations and Inequalities

Problem 13

Chapter 2, Problem 13

Solve each equation. 6(3x-1)= 8 - (10x-14)

Verified step by step guidance

Start by expanding both sides of the equation: on the left side, distribute 6 to both terms inside the parentheses, and on the right side, simplify the expression by distributing the negative sign across the parentheses. This gives you: $6 \times 3x - 6 \times 1 = 8 - 10x + 14$.

Simplify both sides by performing the multiplications and combining like terms: the left side becomes $18x - 6$, and the right side becomes $8 + 14 - 10x$.

Combine the constants on the right side: $8 + 14$ to get $22$, so the equation now is $18x - 6 = 22 - 10x$.

Next, get all the variable terms on one side and constants on the other side. You can do this by adding \$10x$ to both sides and adding $6$ to both sides, resulting in $18x + 10x = 22 + 6$.

Combine like terms on both sides: $28x = 28$. Finally, solve for $x$ by dividing both sides by 28, which gives $x = \frac{28}{28}$.

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Key Concepts

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

Distributive Property

The distributive property allows you to multiply a single term by each term inside parentheses. For example, a(b + c) = ab + ac. This is essential for simplifying expressions like 6(3x - 1) by multiplying 6 with both 3x and -1.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This simplifies expressions and makes solving equations easier, such as combining terms with x on one side of the equation.

Solving Linear Equations

Solving linear equations means finding the value of the variable that makes the equation true. This involves isolating the variable by performing inverse operations like addition, subtraction, multiplication, or division on both sides of the equation.

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