Question

which of the following equations are equivalent? select three options.
□ 2 + x = 5
□ x + 1 = 4
□ 9 + x = 6
□ x + (-4) = 7
□ -5 + x = -2

Explanation:

Step1: Solve each equation for x

For \(2 + x = 5\): Subtract 2 from both sides, \(x = 5 - 2 = 3\).
For \(x + 1 = 4\): Subtract 1 from both sides, \(x = 4 - 1 = 3\).
For \(9 + x = 6\): Subtract 9 from both sides, \(x = 6 - 9 = -3\).
For \(x + (-4) = 7\): Add 4 to both sides, \(x = 7 + 4 = 11\).
For \(-5 + x = -2\): Add 5 to both sides, \(x = -2 + 5 = 3\).

Step2: Identify equations with \(x = 3\)

The equations \(2 + x = 5\), \(x + 1 = 4\), and \(-5 + x = -2\) all have \(x = 3\), so they are equivalent.

Answer:

A. \(2 + x = 5\), B. \(x + 1 = 4\), E. \(-5 + x = -2\)