Question

evaluate independent practice preliminary topics homework complete problems a3, a4, ab, a33 - a40 for independent practice. when you are finished, check the solutions with your teacher. write the property that justifies each step. a3) $3x - 12 = 7x + 8$ $-4x - 12 = 8$ $-4x = 20$ $x = -5$ a4) $5(x - 1) = 4x + 13$ $5x - 5 = 4x + 13$ $x - 5 = 13$ $x = 18$ lifelong learning integrated math 1 b credit 2

Explanation:

Step1: A3 Step1: Identify starting equation

$3x - 12 = 7x + 8$
Justification: Given equation

Step2: A3 Step2: Subtract $7x$ from both sides

$-4x - 12 = 8$
Justification: Subtraction Property of Equality

Step3: A3 Step3: Add 12 to both sides

$-4x = 20$
Justification: Addition Property of Equality

Step4: A3 Step4: Divide by $-4$

$x = -5$
Justification: Division Property of Equality

Step5: A4 Step1: Identify starting equation

$5(x - 1) = 4x + 13$
Justification: Given equation

Step6: A4 Step2: Distribute 5 to terms inside

$5x - 5 = 4x + 13$
Justification: Distributive Property

Step7: A4 Step3: Subtract $4x$ from both sides

$x - 5 = 13$
Justification: Subtraction Property of Equality

Step8: A4 Step4: Add 5 to both sides

$x = 18$
Justification: Addition Property of Equality

Answer:

A3)

1. $3x - 12 = 7x + 8$: Given equation
2. $-4x - 12 = 8$: Subtraction Property of Equality
3. $-4x = 20$: Addition Property of Equality
4. $x = -5$: Division Property of Equality

A4)

1. $5(x - 1) = 4x + 13$: Given equation
2. $5x - 5 = 4x + 13$: Distributive Property
3. $x - 5 = 13$: Subtraction Property of Equality
4. $x = 18$: Addition Property of Equality