Final answer:
To solve the equation 8(x + 3) − 2x = 3x + 9, distribute the 8, combine like terms, rearrange to isolate x, and then solve for x. Verifying by substituting x back into the equation confirms x = -5 is the correct solution.
Step-by-step explanation:
Steps to Solve the Equation 8(x + 3) − 2x = 3x + 9
The first step in solving an equation is to identify the unknown, which in this case is the variable x. Next, we identify the knowns, which are the numbers provided in the equation. The student then needs to choose an equation, plug in the knowns, and solve for the unknown.
- First, distribute the 8 to both terms inside the parentheses: 8x + 24− 2x.
- Simplify the equation by combining like terms: 6x + 24 = 3x + 9.
- Next, get all terms containing x on one side by subtracting 3x from both sides: 3x + 24 = 9.
- Isolate x by subtracting 24 from both sides: 3x = -15.
- Divide both sides by 3 to solve for x: x = -5.
Finally, check the answer to ensure it makes sense by plugging it back into the original equation:
8(-5 + 3) - 2(-5) = 3(-5) + 9
8(-2) + 10 = -15 + 9
-16 + 10 = -6
-6 = -6
This confirms that x = -5 is the correct solution.