15.) $4 x-7=-15+3 x$
16.) $-2-5 x=-4 x-6+5$

Solve the first equation 4 x − 7 = − 15 + 3 x by subtracting 3 x from both sides and adding 7 to both sides, resulting in x = − 8 .
Solve the second equation − 2 − 5 x = − 4 x − 6 + 5 by simplifying the right side, adding 4 x to both sides, and adding 2 to both sides, resulting in x = − 1 .
The solution to the first equation is x = − 8 .
The solution to the second equation is x = − 1 , so the final answers are − 8 , − 1 ​ .

Explanation

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

Solving the First Equation Let's solve the first equation: 4 x − 7 = − 15 + 3 x .


Subtract 3 x from both sides: 4 x − 3 x − 7 = − 15 + 3 x − 3 x x − 7 = − 15 Add 7 to both sides: x − 7 + 7 = − 15 + 7 x = − 8 So, the solution to the first equation is x = − 8 .

Solving the Second Equation Now, let's solve the second equation: − 2 − 5 x = − 4 x − 6 + 5 .

Simplify the right side: − 2 − 5 x = − 4 x − 1 Add 4 x to both sides: − 2 − 5 x + 4 x = − 4 x + 4 x − 1 − 2 − x = − 1 Add 2 to both sides: − 2 − x + 2 = − 1 + 2 − x = 1 Multiply both sides by − 1 :
x = − 1 So, the solution to the second equation is x = − 1 .

Final Answer Therefore, the solutions to the two equations are x = − 8 and x = − 1 .

Examples
Linear equations are used in various real-life scenarios, such as calculating the cost of items, determining the distance traveled at a constant speed, or converting between different units of measurement. For example, if you know the hourly rate and the total earnings, you can use a linear equation to find the number of hours worked. Understanding how to solve linear equations is a fundamental skill that can be applied in many practical situations.

Answered by GinnyAnswer | 2025-07-08