Use the following step as a guide to solve the following equation. Write out your work for all steps to solve the equation.
2x - 5 = 3(4x + 5)
1. Start by distributing the 3 to both terms inside the parentheses:
2x - 5 = 3 * 4x + 3 * 5
2x - 5 = 12x + 15
2. Combine like terms on the right side of the equation:
2x - 5 = 12x + 15
-5 - 15 = 12x - 2x
-20 = 10x
3. Divide both sides of the equation by 10 to solve for x:
-20/10 = 10x/10
-2 = x
So the solution to the equation is x = -2.
Step 1: Distribute the 3 on the right side of the equation:
2x - 5 = 12x + 15
Step 2: Move the variable terms to one side of the equation and the constant terms to the other side of the equation:
2x - 12x = 15 + 5
Simplify:
-10x = 20
Step 3: Divide both sides of the equation by -10 to isolate the variable:
-10x / -10 = 20 / -10
Simplify:
x = -2
Step 4: Check the solution by substituting the value of x back into the original equation:
2(-2) - 5 = 3(4(-2) + 5)
Simplify:
-4 - 5 = 3(-8 + 5)
-9 = 3(-3)
-9 = -9
Since both sides of the equation are equal, the solution x = -2 is correct.
To solve the equation 2x - 5 = 3(4x + 5), follow these steps:
Step 1: Distribute the 3 on the right side of the equation.
2x - 5 = 3 * 4x + 3 * 5
Simplify: 2x - 5 = 12x + 15
Step 2: Move the variable terms to one side of the equation and the constant terms to the other side by adding or subtracting.
Subtract 12x from both sides: 2x - 12x - 5 = 12x - 12x + 15
Simplify: -10x - 5 = 15
Step 3: Move the constant term to the other side by adding or subtracting.
Add 5 to both sides: -10x - 5 + 5 = 15 + 5
Simplify: -10x = 20
Step 4: Isolate the variable by dividing both sides by the coefficient of x.
Divide by -10: -10x / -10 = 20 / -10
Simplify: x = -2
Therefore, the solution to the equation 2x - 5 = 3(4x + 5) is x = -2.