Solve for x: 5x - 7 = 3x + 5.

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Prepare for the GMAS 6th Grade Mathematics Test with guided quizzes. Study using flashcards and multiple-choice questions with detailed hints. Succeed in your math exam!

Multiple Choice

Solve for x: 5x - 7 = 3x + 5.

Explanation:
Solving a linear equation means isolating the variable by undoing the operations on both sides. First, move the x terms to one side and constants to the other by subtracting 3x from both sides: 5x - 7 = 3x + 5 becomes 2x - 7 = 5. Then add 7 to both sides to get 2x = 12. Finally, divide both sides by 2 to find x = 6. Checking by substitution: 5(6) - 7 = 30 - 7 = 23 and 3(6) + 5 = 18 + 5 = 23, which match, confirming x = 6. The other values wouldn’t satisfy the equality when substituted, so they don’t solve the equation.

Solving a linear equation means isolating the variable by undoing the operations on both sides. First, move the x terms to one side and constants to the other by subtracting 3x from both sides: 5x - 7 = 3x + 5 becomes 2x - 7 = 5. Then add 7 to both sides to get 2x = 12. Finally, divide both sides by 2 to find x = 6. Checking by substitution: 5(6) - 7 = 30 - 7 = 23 and 3(6) + 5 = 18 + 5 = 23, which match, confirming x = 6. The other values wouldn’t satisfy the equality when substituted, so they don’t solve the equation.

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