7.) $-15-x=-2x-2x$
8.) $-5x+5x+10=x+2$

Solve the first equation − 15 − x = − 2 x − 2 x by simplifying and isolating x .
Simplify the equation to − 15 − x = − 4 x , then add 4 x to both sides to get − 15 + 3 x = 0 .
Add 15 to both sides to obtain 3 x = 15 , and divide by 3 to find x = 5 .
Solve the second equation − 5 x + 5 x + 10 = x + 2 by simplifying and isolating x .
Simplify the equation to 10 = x + 2 , then subtract 2 from both sides to find x = 8 .
The solutions are 5 , 8 ​ .

Explanation

Problem Analysis We are given two equations to solve for x .

Equation 1: − 15 − x = − 2 x − 2 x Equation 2: − 5 x + 5 x + 10 = x + 2

Solving Equation 1 Let's solve the first equation: − 15 − x = − 2 x − 2 x − 15 − x = − 4 x Add 4 x to both sides: − 15 − x + 4 x = − 4 x + 4 x − 15 + 3 x = 0 Add 15 to both sides: − 15 + 3 x + 15 = 0 + 15 3 x = 15 Divide both sides by 3 :
3 3 x ​ = 3 15 ​ x = 5

Solving Equation 2 Now, let's solve the second equation: − 5 x + 5 x + 10 = x + 2 10 = x + 2 Subtract 2 from both sides: 10 − 2 = x + 2 − 2 8 = x x = 8

Final Answer Therefore, the solutions to the two equations are x = 5 and x = 8 .


Examples
Understanding how to solve linear equations is fundamental in many real-world applications. For instance, consider a scenario where you are managing a budget. If you know your total income and fixed expenses, you can use linear equations to determine how much you can spend on variable expenses while still saving a certain amount. Similarly, in physics, linear equations are used to model motion with constant velocity, allowing you to calculate distances, speeds, or times. These skills are also crucial in fields like economics, engineering, and computer science, where mathematical models often rely on solving equations to make predictions and decisions.

Answered by GinnyAnswer | 2025-07-08