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

The solutions to the equations are x = 5 for the first equation and x = 8 for the second equation.
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Answered by Anonymous | 2025-07-08

5 , 8 ​

Explanation

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


− 15 − x = − 2 x − 2 x

− 5 x + 5 x + 10 = x + 2



Solving the First Equation Let's solve the first equation:

− 15 − x = − 2 x − 2 x
Simplify the right side:
− 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:
3 x = 15
Divide both sides by 3 :
x = 3 15 ​
x = 5

Solving the Second Equation Now let's solve the second equation:

− 5 x + 5 x + 10 = x + 2
Simplify the left side:
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 crucial in many real-world applications, such as calculating distances, determining costs, and modeling various phenomena. For instance, if you are planning a road trip and know the speed you'll be traveling and the total distance, you can use a linear equation to determine how long the trip will take. Similarly, in business, linear equations can help you calculate profits, losses, and break-even points, providing valuable insights for decision-making.

Answered by GinnyAnswer | 2025-07-08