Question

the equation is 5x - 3x + 4. which elements are true?

• the solution is x=6
• the coefficient of x on the left side after subtracting 3x from both sides is 8
• after combining like terms, the equation becomes 2x - 8 = 4
• the final step is to divide both sides by 5

Explanation:

Step1: Start with the given equation

$$5x - 8 = 3x + 4$$

Step2: Subtract $3x$ from both sides

$$5x - 3x - 8 = 3x - 3x + 4$$
$$2x - 8 = 4$$

Step3: Add 8 to both sides

$$2x - 8 + 8 = 4 + 8$$
$$2x = 12$$

Step4: Divide both sides by 2

$$x = \frac{12}{2} = 6$$

Step5: Verify each statement

1. Solution $x=6$: True (matches Step4 result)
2. Coefficient of $x$ after subtracting $3x$: Left side is $2x$, coefficient is 2, not 8: False
3. Combined like terms gives $2x-8=4$: True (matches Step2 result)
4. Final step divide by 5: False (final step divides by 2)

Answer:

• The solution is x=6
• After combining like terms, the equation becomes 2x-8=4