Question

1. write the property that justifies each step. solve $4x - 10 = 5x + 17$.

$4x - 10 = 5x + 17$

$-1x - 10 = 17$

$-1x = 27$

$x = -27$

Explanation:

Step1: State original equation

$4x - 10 = 5x + 17$
Justification: Given equation

Step2: Subtract $5x$ from both sides

$4x - 5x - 10 = 17 \implies -1x - 10 = 17$
Justification: Subtraction Property of Equality

Step3: Add 10 to both sides

$-1x - 10 + 10 = 17 + 10 \implies -1x = 27$
Justification: Addition Property of Equality

Step4: Divide by -1 on both sides

$\frac{-1x}{-1} = \frac{27}{-1} \implies x = -27$
Justification: Division Property of Equality

Answer:

1. $4x - 10 = 5x + 17$: Given equation
2. $-1x - 10 = 17$: Subtraction Property of Equality
3. $-1x = 27$: Addition Property of Equality
4. $x = -27$: Division Property of Equality

Final solution: $x=-27$