Problem 286 Solve each linear equation. $$... [FREE SOLUTION]

Chapter 2: Problem 286

Solve each linear equation. $$5(1.2 u-4.8)=-12$$

Short Answer

Expert verified

The solution is $ u = 2 $.

Step by step solution

- Distribute the 5

Multiply 5 by each term inside the parentheses: \[ 5 \times 1.2u - 5 \times 4.8 = -12 \]This simplifies to: \[ 6u - 24 = -12 \]

- Isolate the term with the variable

Add 24 to both sides of the equation to move the constant term to the right: \[ 6u - 24 + 24 = -12 + 24 \]This simplifies to: \[ 6u = 12 \]

- Solve for the variable

Divide both sides of the equation by 6 to isolate the variable $ u $: \[ \frac{6u}{6} = \frac{12}{6} \]This simplifies to: \[ u = 2 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

distributive property

The distributive property is a fundamental principle in algebra. It states that multiplying a number by a sum or difference is the same as distributing the multiplication across each term within the parentheses. This rule can be written as: \[ a(b + c) = ab + ac \]For our exercise, we applied the distributive property to the expression inside the parentheses: \[ 5(1.2u - 4.8) \]To do this, we multiply 5 by both terms inside the parentheses: \[ 5 \times 1.2u - 5 \times 4.8 \]Simplifying those multiplications, we get: \[ 6u - 24 \]This simplifies our equation, making it easier to solve.

isolating the variable

Isolating the variable is a crucial step when solving linear equations. It involves moving all terms containing the variable to one side of the equation and constant terms to the other side. In our example, after applying the distributive property, we have: \[ 6u - 24 = -12 \]To isolate the term with the variable, we add 24 to both sides of the equation: \[ 6u - 24 + 24 = -12 + 24 \]This step eliminates the constant term on the left side and simplifies to: \[ 6u = 12 \]Now, the equation is set up to easily solve for the variable.

simple algebraic equations

Simple algebraic equations involve straightforward operations to find the value of the unknown variable. Once we have isolated the variable term, solving it often requires basic arithmetic. For our equation: \[ 6u = 12 \]To find the value of $u$, we divide both sides by 6: \[ \frac{6u}{6} = \frac{12}{6} \]This simplifies to: \[ u = 2 \]Thus, the solution to our linear equation is: \[ u = 2 \]By following these steps鈥攁pplying the distributive property, isolating the variable, and solving the simplified equation鈥攚e can efficiently solve any simple algebraic equation.

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91影视

Solve each linear equation. $$5(1.2 u-4.8)=-12$$

Short Answer

Step by step solution

- Distribute the 5

- Isolate the term with the variable

- Solve for the variable

Key Concepts

distributive property

isolating the variable

simple algebraic equations

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