Step 1: Distribute the 3 to the terms inside the parentheses:
-5x + 3x + 6 = 20
Step 2: Combine like terms:
-2x + 6 = 20
Step 3: Subtract 6 from both sides to isolate the variable term:
-2x = 14
Step 4: Divide both sides by -2 to solve for x:
x = -7
Justification for Step 1: This step follows the distributive property, which states that when multiplying a number by a sum inside parentheses, you can distribute the multiplication to each term inside the parentheses.
Justification for Step 2: This step combines the like terms -5x and 3x, which means adding or subtracting their coefficients. In this case, -5x + 3x simplifies to -2x.
Justification for Step 3: This step subtracts the constant term 6 from both sides of the equation. This maintains equality since any operation performed on one side of an equation must also be performed on the other side.
Justification for Step 4: This step divides both sides by the coefficient -2 to solve for x. Division is the inverse operation of multiplication, so dividing both sides by -2 isolates x. The division maintains equality since any operation performed on one side of an equation must also be performed on the other side.
Enter your answer and show all the steps that you use to solve this problem in the space provided.
Write the steps in solving -5x + 3 (x + 2)=20
Justify each step with an appropriate property
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