Find the value of x in the equation 5x - 2(3 - x) = 4.

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Question: Find the value of x in the equation 5x - 2(3 - x) = 4.

Options:

Correct Answer: x = 2

Solution:

Distributing gives 5x - 6 + 2x = 4. Combining like terms: 7x - 6 = 4. Thus, 7x = 10, x = 10/7.

Find the value of x in the equation 5x - 2(3 - x) = 4.

Find the value of x in the equation 5x - 2(3 - x) = 4.

Correct Answer: 10/7

Step 1: Start with the equation: 5x - 2(3 - x) = 4.
Step 2: Distribute the -2 to both terms inside the parentheses: 5x - 2 * 3 + 2 * x = 4.
Step 3: Calculate -2 * 3, which is -6, and rewrite the equation: 5x - 6 + 2x = 4.
Step 4: Combine like terms (5x and 2x): (5x + 2x) - 6 = 4, which simplifies to 7x - 6 = 4.
Step 5: Add 6 to both sides of the equation to isolate the term with x: 7x - 6 + 6 = 4 + 6.
Step 6: This simplifies to 7x = 10.
Step 7: Divide both sides by 7 to solve for x: x = 10 / 7.

Algebraic Manipulation – The question tests the ability to manipulate algebraic expressions, including distribution and combining like terms.
Solving Linear Equations – The question assesses the skill of solving for a variable in a linear equation.