2x – 7=5 5. 2x – 7=5 (2x – 7) + 7 = 5+7 2x = 12 Add 7 To Both Sides. Simplify. 2x_12 2 Divide Both Sides By 2. X= Simplify. 6. 6. 2-X=3-2. 2-X+ 2+ 2 -_+ 2-X=3-2x = 3-2x+ =3 Add 2x To Both Sides. Simplify. Subtract 2 From Both Sides. Simplify. 7. 3r +4= 8 7. 8. 7-2x = 4-5x . 00 9. 2(3-4)=68 -12 (Hint: Use The Distributive Property First.) 9. 10. . 10. A
The Correct Answer and Explanation is:
Equation 1:
2x – 7 = 5
Step 1: Add 7 to both sides:
→ 2x−7+7=5+72x – 7 + 7 = 5 + 7
→ 2x=122x = 12
Step 2: Divide both sides by 2:
→ x=122=6x = \frac{12}{2} = 6
✅ Answer: x = 6
Equation 2:
2 – x = 3 – 2x
Step 1: Add 2x to both sides:
→ 2−x+2x=3−2x+2×2 – x + 2x = 3 – 2x + 2x
→ 2+x=32 + x = 3
Step 2: Subtract 2 from both sides:
→ x=1x = 1
✅ Answer: x = 1
Equation 3:
3r + 4 = 8
Step 1: Subtract 4 from both sides:
→ 3r=43r = 4
Step 2: Divide by 3:
→ r=43r = \frac{4}{3}
✅ Answer: r = 4/3
Equation 4:
7 – 2x = 4 – 5x
Step 1: Add 5x to both sides:
→ 7+3x=47 + 3x = 4
Step 2: Subtract 7 from both sides:
→ 3x=−33x = -3
Step 3: Divide by 3:
→ x=−1x = -1
✅ Answer: x = -1
Equation 5:
2(3 – 4) = 6 – 8
Step 1: Simplify inside parentheses:
→ 2(−1)=−22(-1) = -2
Right side: 6−8=−26 – 8 = -2
✅ Answer: -2 = -2 (True Statement)
Solving algebraic equations involves performing the same operation on both sides to maintain equality. This is known as the Balance Method, a core principle in algebra. The goal is to isolate the variable (such as x or r) on one side of the equation.
In the first equation, 2x – 7 = 5, we added 7 to both sides to eliminate the constant on the left. This made the equation easier to solve, showing how inverse operations (like adding to cancel subtraction) are essential. After simplifying, we divided by 2 to isolate x, reaching the solution.
In the second equation, 2 – x = 3 – 2x, we used a combination of addition and subtraction to move variables to one side and constants to the other. This demonstrated the importance of aligning like terms.
The third and fourth equations follow similar steps: combining like terms, using the distributive property where necessary, and applying inverse operations to isolate variables. In 7 – 2x = 4 – 5x, the key step was recognizing we needed to move x terms to the same side before simplifying.
The fifth equation involved the distributive property: multiplying a number outside parentheses across each term inside. Once both sides were simplified, we confirmed the expression was a true statement, which means it holds for any value (an identity).
These steps rely on maintaining the equality of the equation by treating both sides equally. Understanding these principles helps solve any linear equation systematically and builds a strong foundation for more advanced math.
