What is the solution to this equation? 2x + x – 11 + 3 – 7x = 15 O – A. x=-1 O B. – 13 O cx O D. – 23 C. x=23
The Correct Answer and Explanation is:
Let’s solve the equation step by step:
Given equation:2x+x−11+3−7x=152x + x – 11 + 3 – 7x = 152x+x−11+3−7x=15
Step 1: Combine like terms on the left side.
- Combine the x terms:
2x+x−7x=−4x2x + x – 7x = -4x2x+x−7x=−4x - Combine the constants:
−11+3=−8-11 + 3 = -8−11+3=−8
Now rewrite the equation:−4x−8=15-4x – 8 = 15−4x−8=15
Step 2: Solve for x
Add 8 to both sides to move the constant to the right:−4x=15+8⇒−4x=23-4x = 15 + 8 \Rightarrow -4x = 23−4x=15+8⇒−4x=23
Now divide both sides by -4:x=23−4=−234x = \frac{23}{-4} = -\frac{23}{4}x=−423=−423
So, the solution is:x=−234x = -\frac{23}{4}x=−423
Now let’s look at the answer choices:
- A. x = -1
- B. x = -13
- C. x = 0
- D. x = -23
- C. x = 23 (note: C is repeated)
None of these match the correct answer, which is x = -23/4 or -5.75.
Explanation:
This equation involves combining like terms and solving a simple linear equation. When combining variables and constants, it is important to carefully group all the x terms and all the number terms. After simplifying the expression, isolate the variable using inverse operations. In this case, we added 8 to both sides, then divided by -4.
This kind of problem checks basic algebra skills. The error often made is forgetting to combine terms correctly or misapplying the order of operations. Always combine similar terms before moving on to isolate the variable.
Since the answer choices given are all integers and do not include -23/4, none of the provided options is correct.
