Question

what is the first step to solve this equation?
x - 5 = 7 - 2x
add 2x to both sides of
the equation
combine x and -2x
add 7 to both sides of
the equation
subtract 2x from both
sides of the equation

Explanation:

Step1: Analyze the equation structure

The equation is \( x - 5 = 7 - 2x \). To solve for \( x \), we want to get all the \( x \)-terms on one side.

Step2: Evaluate each option

• Option 1: Adding \( 2x \) to both sides: \( x + 2x - 5 = 7 - 2x + 2x \), which simplifies to \( 3x - 5 = 7 \). This helps in combining like terms (all \( x \)-terms on the left).
• Option 2: We can't combine \( x \) (on left) and \( -2x \) (on right) directly as they are on different sides of the equation.
• Option 3: Adding 7 to both sides would give \( x - 5 + 7 = 7 - 2x + 7 \), which complicates the \( x \)-terms separation.
• Option 4: Subtracting \( 2x \) from both sides: \( x - 2x - 5 = 7 - 2x - 2x \), leading to \( -x - 5 = 7 - 4x \), which is not a helpful first step for combining \( x \)-terms.

So the correct first step is to add \( 2x \) to both sides.

Answer:

A. Add 2x to both sides of the equation