4.) [tex]$9 x+5=3 x-19$[/tex]
5.) [tex]$x+8=13+2 x$[/tex]
6.) [tex]$14 x=18+5 x$[/tex]

Solve each equation by isolating x.
Equation 4: 9 x + 5 = 3 x − 19 ⇒ x = − 4 .
Equation 5: x + 8 = 13 + 2 x ⇒ x = − 5 .
Equation 6: 14 x = 18 + 5 x ⇒ x = 2 .
The solutions are x = − 4 , − 5 , 2 ​ .

Explanation

Problem Analysis We are given three linear equations and our goal is to solve each one for the variable x. We will use algebraic manipulation to isolate x on one side of each equation.

Solving Equation 4 For equation 4, we have 9 x + 5 = 3 x − 19 . First, subtract 3 x from both sides to get 6 x + 5 = − 19 . Then, subtract 5 from both sides to get 6 x = − 24 . Finally, divide both sides by 6 to find x = − 4 .

Solving Equation 5 For equation 5, we have x + 8 = 13 + 2 x . Subtract x from both sides to get 8 = 13 + x . Then, subtract 13 from both sides to find x = − 5 .

Solving Equation 6 For equation 6, we have 14 x = 18 + 5 x . Subtract 5 x from both sides to get 9 x = 18 . Then, divide both sides by 9 to find x = 2 .

Final Answer Therefore, the solutions are: Equation 4: x = − 4 Equation 5: x = − 5 Equation 6: x = 2


Examples
Linear equations are used in everyday life to solve problems involving unknown quantities. For example, if you want to determine how many hours you need to work to earn a certain amount of money, you can set up a linear equation where the unknown variable is the number of hours. Similarly, if you are trying to figure out the cost of a taxi ride based on the distance traveled, you can use a linear equation to model the relationship between distance and cost. Understanding how to solve linear equations is a fundamental skill that can be applied to various real-world scenarios.

Answered by GinnyAnswer | 2025-07-08

To isolate x in the equations, we applied basic algebraic manipulation. We found the solutions are x = -4 for equation 4, x = -5 for equation 5, and x = 2 for equation 6. Thus, the results are x = -4, -5, 2.
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Answered by Anonymous | 2025-08-06