Solve $7 x-5 x-3=x+4$
A) $x=-8$
B) $x=6$
C) $x=-10$
D) $x=7$
Answer (1)
Combine like terms: 7 x − 5 x − 3 = 2 x − 3 .
Rewrite the equation: 2 x − 3 = x + 4 .
Isolate x by subtracting x from both sides: x − 3 = 4 .
Solve for x by adding 3 to both sides: x = 7 . The final answer is 7 .
Explanation
Understanding the Problem We are given the equation 7 x − 5 x − 3 = x + 4 . Our goal is to solve for x . We will simplify the equation by combining like terms and isolating x on one side of the equation.
Combining Like Terms First, we combine the x terms on the left side of the equation: 7 x − 5 x = 2 x . So the equation becomes 2 x − 3 = x + 4 .
Isolating x Next, we want to isolate x on one side of the equation. We can subtract x from both sides: 2 x − x − 3 = x − x + 4 , which simplifies to x − 3 = 4 .
Solving for x Now, we add 3 to both sides of the equation to solve for x : x − 3 + 3 = 4 + 3 , which simplifies to x = 7 .
Verification To verify our solution, we substitute x = 7 back into the original equation: 7 ( 7 ) − 5 ( 7 ) − 3 = 7 + 4 , which simplifies to 49 − 35 − 3 = 11 , and 11 = 11 . Since the equation holds true, our solution is correct.
Final Answer Therefore, the solution to the equation 7 x − 5 x − 3 = x + 4 is x = 7 .
Examples
Imagine you're balancing a budget. On one side, you have income and expenses, and on the other side, you have your savings goal. Solving linear equations like this helps you determine how much you need to save each month to reach your goal. For instance, if your income is 7 x , expenses are 5 x + 3 , and your savings goal is x + 4 , solving the equation tells you the value of 'x' that makes your budget balance perfectly. This skill is crucial for managing personal finances and making informed financial decisions.
