Solve the following equation, justify each step with the appropriate property.
5(2x - 3) + 20 = 35
10 x -15 + 20 = 35 distributive
10 x + 5 = 35 add
10 x = 30 add -5 both sides
x = 3 divide
Step 1: Distribute the 5 to the terms inside the parentheses.
10x - 15 + 20 = 35 (Distributive Property)
Step 2: Combine like terms.
10x + 5 = 35 (Combining like terms, -15 + 20 = 5)
Step 3: Subtract 5 from both sides to isolate the variable term.
10x = 30 (Subtraction Property of Equality)
Step 4: Divide both sides by 10 to solve for x.
x = 3 (Division Property of Equality)
Therefore, the solution to the equation 5(2x - 3) + 20 = 35 is x = 3.
To solve the equation 5(2x - 3) + 20 = 35, we will apply the distributive property and simplify the equation step by step. Here's how:
Step 1: Applying the distributive property
5(2x - 3) = 10x - 15
Step 2: Rewriting the equation with the simplified expression
10x - 15 + 20 = 35
Step 3: Combining like terms to simplify the left side of the equation
10x + 5 = 35
Step 4: Isolating the variable on one side of the equation
10x + 5 - 5 = 35 - 5
10x = 30
Step 5: Dividing both sides by 10 to solve for x
10x/10 = 30/10
x = 3
To justify each step with the appropriate property, here's the breakdown:
Step 1: Distributive property - This property states that when you have a number outside parentheses multiplying an expression inside the parentheses, you need to distribute or multiply that number to every term inside the parentheses.
Step 2: No property used - Here, we are simply rewriting the equation with the simplified expression obtained from applying the distributive property.
Step 3: Combining like terms - This process involves adding or subtracting terms with the same variables and exponents.
Step 4: Subtraction property of equality - This property states that you can subtract the same quantity from both sides of an equation without changing its equality.
Step 5: Division property of equality - This property states that you can divide both sides of an equation by the same non-zero number without changing its equality.