Solve for x: 5x + 2 = 3x + 10.

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Question: Solve for x: 5x + 2 = 3x + 10.

Options:

Correct Answer: 4

Solution:

Subtracting 3x from both sides gives 2x + 2 = 10, then subtracting 2 gives 2x = 8, leading to x = 4.

Solve for x: 5x + 2 = 3x + 10.

Solve for x: 5x + 2 = 3x + 10.

Step 1: Start with the equation 5x + 2 = 3x + 10.
Step 2: Subtract 3x from both sides of the equation. This gives you 5x - 3x + 2 = 10.
Step 3: Simplify the left side. 5x - 3x is 2x, so now you have 2x + 2 = 10.
Step 4: Next, subtract 2 from both sides of the equation. This gives you 2x + 2 - 2 = 10 - 2.
Step 5: Simplify again. The left side is 2x and the right side is 8, so now you have 2x = 8.
Step 6: Finally, divide both sides by 2 to solve for x. This gives you x = 8 / 2.
Step 7: Simplify the right side. 8 divided by 2 is 4, so x = 4.

Linear Equations – The question tests the ability to solve a linear equation by isolating the variable.
Algebraic Manipulation – The question assesses skills in performing algebraic operations such as addition, subtraction, and simplification.